Math and Stat Research Day (MSRD)

MSRD is a platform for students and faculty to publicly present their research and scholarly activities in mathematics, statistics and their applications in various fields. The event is open to all UMKC students, faculty and staff.
msrd-logo-1.jpg

 

7th Annual UMKC Math and Stat Research Day

Friday, April 23, 2021
9 a.m. – 4 p.m. US Central Time
Attend on Zoom

MSRD is an annual one-day event celebrating student and faculty research and creative and scholarly activities. The event promotes research in mathematics, statistics and the applications in various fields, and is open to the public.

For this year, there are 18 speakers from different universities including Washington State University, Iowa State University, University of Kansas, University of Missouri-Kansas City, and University of Leicester.

The talks are organized in three themes:

Theme 1: General Math & Stat Research (9:20 AM – 10:40 AM)

Theme 2: COVID-19 in Kansas City (10:40 AM – 2:00 PM)

Theme 3: COVID-19 Pandemic (2:00 PM – 4:00 PM)

Organizers

There is no registration fee. This is a public event — open to all students and researchers.

  • Deadline for abstract submission - April 15, 2021
  • Please email the abstract and title of your research to Majid Bani
  • Notification of acceptance - April 20, 2021

Schedule 

  • Friday, April 23, 2021 (9:00 AM -4:00 PM)
  • Zoom link: https://umsystem.zoom.us/j/97200909775 
  • Each presentation is 15 minutes, plus five minutes for a question-and-answer period
  • Chair of morning session - Sam Ye 
  • Chair of afternoon session - Noah Rhee

 

Introduction

9:00 am-9:20 am Welcome and Opening Remarks (Dr. Majid Bani)       

Theme 1: General Math & Stat (9:20 AM – 10:40 AM) 

9:20 am-9:40 am Exploring the Dynamics of Virulent and Avirulent Aphids: A Case for a “Within Plant" Refuge
Aniket Banerjee, Department of Mathematics, Iowa State University, aniketb@iastate.edu 


9:40 am-10:00 am Dynamics of a Female Harvesting Male Stocking model with weak Allee effects. 
Eric Takyi, Department of Mathematics, Iowa State University, takyiem@iastate.edu 


10:00 am-10:20 am A Novel Mathematical Model to Explain the Changing Language Dynamics in India
Kushani DeSilva, Department of Mathematics, Iowa State University, kdesilva@iastate.edu

 
10:20 am-10:40 am Homoskew-Derivations with Commutativity of Rings
Mehsin Jabel Atteya, School of Mathematics & Actuarial Science, University of Leicester, UK. Email: mjaas2@leicester.ac.uk 


Theme 2: COVID-19 in Kansas City (10:40 AM – 2:00 PM)

10:40 am-11:00 am Seasonal Changes in Kansas City 311 Service Requests
William Ford, UMKC Math & Stat Department,  wandrewford@mail.umkc.edu 


11:00 am-11:20 am Changes in Kansas City 311 Service Requests Due to COVID-19 Pandemic
Thao Tran, UMKC Math & Stat Department thao.tran@mail.umkc.edu 


11:20 am-11:40 am Analyzing Intercorrelated Factors among Kansas City Neighborhoods During the COVID-19 Pandemic
Braeden Vaughn, UMKC Math & Stat Department, bv2my@mail.umkc.edu 


11:40 am-12:00 pm A Prospective Spaciotemporal Analysis to Detect Clusters of COVID-19 in Kansas City, MO 
Hadeel Alqadi, UMKC Math & Stat Department, hadz6@mail.umkc.edu 


12:00 pm-12:20 pm Did the COVID-19 Pandemic Increase Math Anxiety in College Students?
Dilek Soysal, UMKC Math & Stat Department, dswbz@mail.umkc.edu 


1:00 pm-1:20 pm Statistical Analysis of Kansas City COVID-19 Data with Respect to Race, Ethnicity, Age, and Gender       
Sindhu Balakumar, UMKC Math & Stat Department, sbmbg@mail.umkc.edu 


1:20 pm-1:40 pm Time Series Analysis of COVID-19 Cases in Kansas City, Missouri
Siqi Wu, UMKC Math & Stat Department, sw4fc@mail.umkc.edu 


1:40 pm-2:00 pm Evaluating the Spatial Clusters of COVID-19 with Respect to Demographic Factors in Kansas City, MO
Hadeel Alqadi, UMKC Math & Stat Department, hadz6@mail.umkc.edu 


Theme 3: COVID-19 Pandemic (2:00 PM – 4:00 PM)

2:00 pm-2:20 pm Google Health Trends and COVID-19 Case Incidence in Africa: A Useful Surveillance Tool?      
Alexander Fulk, Department of Ecology & Evolutionary Biology,University of Kansas, alxjfulk@gmail.com 

2:20 pm-2:40 pm Exploring the Role of Superspreading Events in SARS-CoV-2 Outbreaks
Jordan Bramble, Department of Mathematics, University of Kansas, missylink@ku.edu 

 
2:40 pm-3:00 pm Covid-19: The Role of Changing Behavior, Public Sentiments, and Risk Perception on Disease Transmission       
Folashade Agusto, Department of Ecology & Evolutionary Biology, University of Kansas, fbagusto@gmail.com 


3:00 pm-3:20 pm The Kansas Mask Experiment: The Impact of Mask Compliance in Kansas Counties on the Spread of COVID-19
Stephen Gardner, UMKC Math & Stat Department, ssgzt2@mail.umkc.edu 

3:20 pm-3:40 pm Automatic Detection of COVID-19 Using Data Extracted from Chest X-ray Images
Grace Reesman, UMKC Math & Stat Department  graceklausen@mail.umkc.edu 

3:40 pm-4:00 pm Deterministic and Stochastic Models for the Epidemic Dynamics of COVID-19 in Wuhan, China
Jordan Culp, Math & Stat Department, Washington State University, jordan.culp@wsu.edu     

 

Titles and Abstracts

9:20 am-9:40 am

Exploring the Dynamics of Virulent and Avirulent Aphids: A Case for a “Within Plant" Refuge

Aniket Banerjee
Department of Mathematics
Iowa State University
aniketb@iastate.edu

 

The Soybean Aphid is the chief invasive pest plaguing Soybean agriculture, particularly in the Midwestern United States. A tactic to counter the pest is genetic modification of the Soybean plant, making it resistant to certain Aphid bio-types. Colonization and feeding by an Aphid can alter a plant's physiology, primarily by two mechanisms, feeding facilitation and the obviation of resistance. This in turn favors subsequent colonization by additional conspecifics. We develop a non-local population model, which displays the dynamics of these biological mechanisms. We perform numerical simulations via the model which successfully mimic aphid dynamics observed in the field. Our results are motivation for the possibility of a \Within Plant" Refuge.

 

 

9:40 am-10:00 am

Dynamics of a Female Harvesting Male Stocking model with weak Allee effects.

Eric Takyi
Department of Mathematics
Iowa State University
takyiem@iastate.edu

 

Female Harvesting Male Stocking (FHMS) is a control method first proposed by Jingjing Lyu in mimicking the Trojan Y-Chromosome strategy for invasive fish eradication as it skews the population sex ratio to-

wards males and hence causing extinction over time. In this talk, we incorporate a weak Allee component into the female population and study the dynamical properties of the model. Allee effects are said to be weak when a population growth rate remains positive but at lower densities. We include a spatial component to the model (FHMS + weak Allee effect) and observe the emergence of Turing patterns. We discuss applicability to large scale bio-control.

 

10:00 am-10:20 am

A Novel Mathematical Model to Explain the Changing Language Dynamics in India

Kushani DeSilva
Department of Mathematics
Iowa State University
kdesilva@iastate.edu

Classical language dynamics models explain how one language, gains speakers over another language. The “winner” typically is the higher status language, as seen with English outcompeting languages such as Scottish Gaelic, Welsh, and Mandarin.

However, various local ecological factors may work to compete against the high-status language. We showcase such an example in India using census data, where Hindi

has started to outcompete the higher-status English language. To this end a novel mathematical model is proposed and analyzed.

 

10:20 am-10:40 am

Homoskew-Derivations with Commutativity of Rings

Mehsin Jabel Atteya
School of Mathematics & Actuarial Science
University of Leicester, UK
mjaas2@leicester.ac.uk

One of the natural questions of Ring Theory is to determine conditions implying commutativity of the ring. During the last two decades, the commutativity of associative rings with derivations have become one of the focus points of several authors and significant work has been done in this direction. The study of derivation was initiated during the 1950s and 1960s. Derivations of rings got a tremendous development in 1957 when Posner [1] established two very striking results in the case of prime rings.  In 2000, El Sofy [2] defined a homoderivation on R as an additive mapping h: R⟶R satisfying h(xy)=h(x)h(y)+h(x)y+xh(y) for all x, y ∈ R while in 2020, Mehsin Jabel Atteya [3] introduced the definition of (σ, τ)-Homgeneralized derivations of semiprime rings with some results. Furthermore, in 2021, Mehsin Jabel Atteya [4] study the behavior of skew-Homogeneralized derivations of rings and presented some results concerning that.

The main purpose of this paper is to introduce the definition of a Homoskew-derivations of rings with some results. Precisely, we prove the commutativity of a ring R which satisfied certain conditions These results are in the sprite of the well-known theorem of the commutativity of prime and semiprime rings with derivations satisfying certain polynomial constraints.

[1] E.C. Posner, “Derivations in prime rings”, Proc. Amer. Math. Soc.8 (1957), 1093- 1100.

[2] M.M. El Sofy Aly, “Rings with some kinds of mappings”, M.Sc. Thesis, Cairo University, Branch of Fayoum, (2000).

[3] Mehsin Jabel Atteya, “(σ, τ)-Homgeneralized Derivations of Semiprime Rings”, 13th Annual Binghamton University Graduate Conference in Algebra and Topology (BUGCAT), The State University of New York, USA, November 7- 8, and November 14-15, (2020).

[4] Mehsin Jabel Atteya, “Skew-Homogeneralized Derivations of Rings”, MATH FOR ALL in New Orleans Conference, Tulane University Math Department, 5th-7th March (2021). 

 

 10:40 am-11:00 am

Seasonal Changes in Kansas City 311 Service Requests

William Ford
UMKC Math & Stat Department 
wandrewford@mail.umkc.edu

Members of a community need a way to communicate with their local government in order to request common services. At the same time, local government needs a way to anticipate changes in these requests in order to better allocate resources and more efficiently serve the public. Kansas City Missouri (KCMO) established the 311 hotlines to provide an easy way to report non-emergency problems, request service, and ask questions about city services. Since its inception, it has expanded to receiving reports by email, website, and even phone apps. In this study, we looked at 311 data for KCMO and analyzed which city services were most commonly used and how their use changed in warm months (March – August 2019) compared to cold months (September 2019 – February 2020). Understanding how the seasons affect the requested services would better prepare the city to allocate resources and respond to service requests. Our main findings indicated that the total number of service requests declines in colder months, but not uniformly across all categories. Most notably, “Mowing and Weeds” had a sharp decline in cold months, but “Trash and Recycling” requests had the highest number of service requests in December compared to every other month in 2019.

 

11:00 am-11:20 am        

Changes in Kansas City 311 service requests due to COVID-19 Pandemic

Thao Tran
UMKC Math & Stat Department
thao.tran@mail.umkc.edu

The COVID-19 pandemic and control measure such as social distancing have brought abrupt changes to American day-to-day lives. The effects of heightened health risks and lock down orders on families are markedly reflected in their demands for city services. In this study, we use the Kansas City-Missouri (KCMO) 311 data to compare the trends and composition of service requests before the pandemic (March - August, 2019) and during the pandemic (March - August, 2020). The difference in these trends would help us understand how people’s demands for city service have been impacted and provide insights to a better reallocation of resources for the 311 service in KCMO in response to future pandemics. Our main findings show that the overall number of service requests declined sharply during the pandemic, especially between March and May, but the decline is not unanimous across different categories. In particular, we find significant reduction in service requests related to “Street Conditions” and “Animals control”, while “Public Health” requests doubled and “Public Safety” requests tripled.

 

11:20 am-11:40 am

Analyzing Intercorrelated factors among Kansas City neighborhoods during the COVID-19 Pandemic

Braeden Vaughn
UMKC Math & Stat Department
bv2my@mail.umkc.edu  

In the interest of studying socioeconomic factors, examining data for specific Kansas City neighborhoods can give one a more precise view of the characteristics of the city as opposed to looking at each variable at the city-wide level. One issue with using this method is that one will end up with a large matrix of data, in this case a 200 x 17 matrix. The following method will work on matrices much larger as well. 

17 variables were collected for around 200 neighborhoods. Using singular value decomposition, the number of variables used to describe the neighborhoods could be reduced. Specifically, Principal Component Analysis was used to construct new variables that are correlated with the original descriptors. This dimensionality reduction minimized the amount of information lost and returned new variables. After the reduction, two principal components were constructed that explained a little over half of the variance in the original data. While this is lower than would be preferred, it provided components with high correlation to certain variables in the data and which were easy to interpret. 

 

11:40 am-12:00 pm

A Prospective Spaciotemporal Analysis to Detect Clusters of COVID-19 in Kansas City, MO

Hadeel Alqadi  
UMKC Math & Stat Department
hadz6@mail.umkc.edu

COVID-19 is an infectious disease caused by the severe acute respiratory syndrome novel coronavirus (SARS-CoV-2). Just in the US, the COVID-19 cases are over 30 million and more than 549,000 deaths as of March 2021. We conducted a prospective spatial-temporal analysis of Kansas City, MO COVID-19 data at the zip code level. The analysis was focused on daily COVID-19 cases in four equal periods of three months. We detected temporal patterns of emerging and reemerging space-time clusters during March 2020-Fabruary 2021.  In the first period, 3 statistically significant clusters emerged, which were mainly concentrated in the downtown Kansas City, MO. In the second period, it increased to 7 clusters, spreading a wider region in the downtown and north of Kansas City. In the third period, there were 9 clusters covering large areas of north and downtown Kansas City, Missouri. In the last period, 10 clusters were present and further extended the infection along the state line.  The statistical results can provide guidance for public health officials and decision-makers to improve the allocation of resources (e, g, vaccine, and testing sites) and implement more control measures in the areas that have been affected the most. As more data becomes available, the statistical clustering can be used as a COVID-19 surveillance tool.

 

12:00 pm-12:20 pm

Did the COVID-19 Pandemic Increase Math Anxiety in College Students?

Dilek Soysal
UMKC Math & Stat Department
dswbz@mail.umkc.edu

This study used weekly survey data collected from 53 (34 male and 19 female) undergraduate students in summer 2020 to investigate math anxiety during the COVID-19 pandemic. Freshman and sophomore students had the highest prevalence of increased math anxiety due to the COVID-19 pandemic. The time-series data indicate fluctuations in the level of math anxiety with substantially increased levels prior to the midterm and final exams. Furthermore, the survey data shows a significant reduction in the use of academic support (supplemental instruction and tutoring) during the summer 2020 semester. 

 

1:00 pm-1:20 pm

Statistical Analysis of Kansas City COVID-19 Data with Respect to Race, Ethnicity, Age, and Gender           

Sindhu Balakumar
UMKC Math & Stat Department
sbmbg@mail.umkc.edu

 COVID-19 is a respiratory infection that has resulted in a deadly pandemic dominating the world. The main objective of this study was to determine if COVID-19 disproportionately impacted certain minority communities. We obtained raw data of confirmed COVID-19 cases in Kansas City, Missouri from March 2020 to October 2020. Our statistical analysis shows that individuals between the ages of 20-29 years had the highest frequency of COVID-19 cases. Nevertheless, the average age of COVID positive Hispanic/Latino individuals was significantly lower than both African American and White individuals. Hispanic/Latino individuals also had the highest prevalence of COVID-19 positive cases than both White and African American individuals in Kansas City. Moreover, by using ANOVA testing, we found that females had a significantly higher prevalence in COVID positive cases and mortality than men. In conclusion, we observed that COVID-19 has impacted individuals who are Hispanic/Latino, female, or between the ages of 20-29 more than other groups.

 

1:20 pm-1:40 pm

Time Series Analysis of COVID-19 Cases in Kansas City, Missouri

Siqi Wu,
UMKC Math & Stat Department,
sw4fc@mail.umkc.edu

The COVID-19 pandemic has affected the entire world. As of March 2021, more than 30 million cases and 541 thousand deaths have been reported. The first case of COVID-19 in the US was reported on January 21, 2020.  In this talk, I will present time series analysis of COVID-19 cases in Kansas City, Missouri with respect to zip code, gender, race, and ethnicity. The Time series analysis displays the trend and temporal patterns of COVID-19 cases in Kansas City. We found that the prevalence of COVID-19 was first the highest in the Jackson county and thereafter in the Clay county. The time series data also shows that the prevalence of COVID-19 was constantly higher in the Hispanic population.

 

1:40 pm-2:00 pm

Evaluating the spatial clusters of COVID-19 with respect to demographic factors in Kansas City, MO

Hadeel Alqadi,  
UMKC Math & Stat Department,
hadz6@mail.umkc.edu

During an emerging pandemic like COVID-19, it is critical to implement spatial surveillance that can identify clusters of the hardest-hit areas. Cluster detection can be used as a guiding tool to reduce the chances of another wave, to avoid the rise of small local outbreaks, and ultimately to control the epidemic. Research suggest that certain racial and ethnic minority groups may have been disproportionately impacted by the spread of COVID-19. In the present study, we used the spatial data to observe differences in the COVID-19 clusters with respect to rage, gender, and ethnicity. Specifically, we utilized a retrospective spatial analysis of Kansas City, MO COVID-19 data at the zip code level during March - November 2020. Our statistical results indicate that the cluster of male population is more scattered, however female population had higher prevalence. The clusters Hispanic population had the highest prevalence and were also more scattered. The statistical results can provide guidance for public health officials and decision-makers to improve the allocation of resources and to correctly implement the COVID-19 vaccine to priority groups.

 

2:00 pm-2:20 pm

Google Health Trends and COVID-19 Case Incidence in Africa: A Useful Surveillance Tool?        

 Alexander Fulk,
Department of Ecology & Evolutionary Biology
University of Kansas alxjfulk@gmail.com

In this research, our objective was to use Google Health Trends (GHT) to anticipate and characterize COVID-19 incidence across Africa. To pursue this goal, we collected the number of searches from the GHT data-source related to COVID-19 using four terms, namely ‘coronavirus’, ‘coronavirus symptoms’, ‘COVID19’, and ‘pandemic’. The terms were correlated to weekly COVID-19 case incidences for 54 countries in Africa at the national level, between February, 2020 to January, 2021 via a multiple linear regression analysis. We also collected 72 other variables relating to demographics, economics, internet accessibility, and disease burden, among other predictors for each country, to characterize the mechanisms that might explain the relationship between GHT searches and COVID-19 incidence. Average case and death incidences were also calculated over 4 different time periods as a measure of which countries were more affected during the interval studied. Our study shows that GHT lacked the predictive power to anticipate COVID-19 cases in most African countries, and its lack of applicability was not explained by any of the analyzed indicators either normally distributed, or log-adjusted. We further observed that GHT may best be used during the early stages of an outbreak when infection growth coincides with high search volume for disease specific terms. Furthermore, GHT performed poorly in countries that did not have rapid infection growth until much later.

 

2:20 pm-2:40 pm

Exploring the Role of Superspreading Events in SARS-CoV-2 Outbreaks 

Jordan Bramble
Department of Mathematics
University of Kansas, missylink@ku.edu 

The novel coronavirus SARS-CoV-2 emerged in China’s Hubei province in the winter of 2019 and subsequently spread throughout the world. With over 30 million cases, the U.S. has been hit especially hard. However, SARS-CoV-2 outbreak profiles have varied greatly both by country and, in the U.S., by state. Motivated by the contribution of superspreading events (SSE) – defined here as social gatherings that result in multiple infections – to SARS-CoV-2 spread, we formulate a continuous-time Markov chain model that incorporates SSE-related infections in such a way that their influence on outbreak dynamics may be investigated relative to that of non-SSE-related infections. Three versions of the model – one with control measures and two without – are simulated using Gillespie’s direct algorithm. Results indicate that SSEs contribute to variability in outbreak profiles. This variability has important public health implications, as it limits prediction robustness and complicates management strategies, and these implications suggest a heightened need for targeted control of SSEs.  

 

2:40 pm-3:00 pm

Covid-19: The Role of Changing Behavior, Public Sentiments, and Risk Perception on Disease Transmission                                                                                                   

Folashade Agusto
Department of Ecology & Evolutionary Biology
University of Kansas
fbagusto@ku.edu

COVID-19 is a respiratory disease caused by coronavirus, SARSCOV2. The disease has led to over 81 million cases, and with over 2 million deaths worldwide. In the current social and political climate, the risk of COVID-19 infection is driven by people’s perception of risk of the infection. A number of factors drive public perception of disease risk, these include people’s beliefs, knowledge, and information about a disease. In this talk, I present two different models for COVID-19 looking at peoples’ behavior and their sentiments about the disease. One model uses game theory and appropriate payoff functions relating to the perception of risk measured using disease incidence and severity of infection to account for a series of human behaviors. Which leads to a complex interplay between the epidemiological model, that affects success of different strategies, and the game theoretic behavioral model, which in turn affects the spread of the disease. The second model uses tweets from twitter to account for peoples’ sentiments about the disease. It also takes into account negative sentiments driven by misinformation. The results from these models shows that rational behavior of susceptible individuals can lead to a second wave of the pandemic. To reduce the burden of the disease in the community, it is necessary to ensure positive sentiments and feelings and to incentivize such altruistic behavior by infected individuals as voluntary self-isolation.

 

3:00 pm-3:20 pm

The Kansas Mask Experiment: The Impact of Mask Compliance in Kansas Counties on the Spread of COVID-19

Stephen Gardner,
UMKC Math & Stat Department,
ssgzt2@mail.umkc.edu  

COVID-19 has emerged as a serious threat to public health in the United States and all over the world with over 2.7 million dead as of 3-21-2021 according to the WHO. Some efforts to control the spread of COVID-19, such as wearing masks or face coverings, have proven controversial in the U.S. with CDC guidance on mask usage changing over time, and with some portions of the population being unwilling to wear face coverings altogether. As cases of COVID-19 surged in the Spring of 2020, Kansas Governor Laura Kelly issued executive order #20-52 (the order) requiring most Kansans to wear masks in public places starting on July 3, 2020 to help prevent the spread of the virus. 21 Kansas counties complied with the order and 84 did not, and in the weeks that followed the order a natural experiment occurred allowing researchers to estimate the impact that mask wearing had on the spread of COVID-19 in Kansas counties. Using weekly data from the Kansas Department of Health (KDHE) over the period 5-1-2020 to 9-25-2020, this paper uses linear regression (essentially difference-difference estimation) to estimate the growth rate of COVID-19 cases in Kansas counties that complied with the order compared to counties that did not comply with the order. This analysis finds that counties that complied with the mask order experienced COVID-19 growth rates that were between 21 and 45 percentage points lower compared to counties that did not comply with the order. 

 

3:20 pm-3:40 pm

Automatic Detection of COVID-19 Using Data Extracted from Chest X-ray Images

Grace Reesman,
UMKC Math & Stat Department
 graceklausen@mail.umkc.edu

The COVID-19 pandemic has already infected millions and claimed thousands of lives. Therefore, the ability to accurate rapid screening could greatly assist healthcare professionals in diagnosing COVID-19 and resolve current diagnostic issues. Machine learning has been particularly useful in previous instances of image processing and analysis, and could aide in COVID-19 screening procedures. In this analysis, we created two models that can diagnose COVID-19 based o_ of x-ray images of lungs. The x-ray images for both COVID-19 infected and normal lungs used in this analysis were taken from the COVID-19 Radiography Database. The first is a decision tree which was able to correctly COVID infected lungs in 77.3% of cases and uninfected lungs in 88.7% of cases. Overall, the decision tree correctly classified lungs as COVID infected or uninfected lungs in 83% of cases. The second model we created was a multi-layer perceptron neural network. We found that this neural network was able to differentiate between normal and COVID infected lung x-rays 77.7% of the time in testing.

 

3:40 pm-4:00 pm

Deterministic and Stochastic Models for the Epidemic Dynamics of COVID-19 in Wuhan, China

Jordan Culp,
Math & Stat Department,
Washington State University,
jordan.culp@wsu.edu  

In this talk I will present deterministic and stochastic models proposed to study the transmission dynamics of COVID-19 in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number R0 serves as a sharp disease threshold: the disease dies out if R0 < 1 and persists if R0 > 1. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when R0 > 1. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly.

 

 

 

MSRD Archives

View the recorded Zoom session

Schedule of Presentations  
9:30 am 9:40 am Welcome and Opening Remarks
9:40 am 10:00 am Grace Reesman, UMKC Physics & Astronomy Department, Method of Attaining Quadrupole Deformation Parameters in 73As
10:00 am 11:00 am Dr. Folashade Agusto, KU Department of Ecology & Evolutionary Biology, University of Kansas, Optimal Control of Malaria Across Sub-Saharan Africa Temperature Gradient
11:00 am 11:25 am Lucas Delibas, Bryan Harris & Rylan Sampson, UMKC Math & Stat Department, Modeling COVID-19 Outbreak: A Cross-Species Approach
11:25 am 11:50 am Vanessa R. Collins, UMKC School of Business, News Corporation Spinoff of 21st Century Fox and The New News Corp: An Event Study
12:20 pm 12:45 pm Matthew Shirley, UMKC Math & Stat Department,  A Mathematical Model for Examining the Effects of Drug-Resistant Salmonella in Developing Countries
12:45 pm 1:30 pm Dilek Soysal, Arash Arjmand & Deepak Sireeshan, UMKC Math & Stat Department,  A Mathematical Model to Investigate Epidemic Waves of Math Anxiety
1:30 pm 2:15 pm Kodi Kuhlmann, UMKC Math & Stat Department, A SEIQR Model to Investigate Travel Dynamics from City of COVID-19 Origin to Rest of World
2:15 pm 3:00 pm Pleasance Mertz, UMKC Math & Stat Department, Simulations and Analysis of COVID-19 Spread: Lessens to be learned
3:00 pm 3:25 pm Benjamin Floyd, UMKC Physics & Astronomy Department, Dependence of AGN Activity on Cluster Mass and Cosmological Distance in the SPT Cluster Surveys
3:25 pm 3:50 pm Mostafa Badroddin & ZhiQiang Chen School of Computing and Engineering, Civil and Mechanical Engineering Department, Application of Poisson Process for Seismic Ground Simulation and Life-cycle Multi-hazard Bridge Resilience Assessment

Method of Attaining Quadrupole Deformation Parameters in 73As

Grace Reesman, UMKC Physics and Astronomy Department

Only two nuclei in the mass A = 70 region (67Cu and 71As) are known to exhibit large deformation as a result of a proton occupying the f7/2 orbital. The goal of this work was to infer the underlying deformation of 73As by measuring as many lifetimes as possible in an attempt to understand the structure of this nucleus. Coincidence matrices were constructed from these measured γ-γ coincidences for detectors at 35 degrees, 90 degrees, and 145 degrees relative to the incoming beam direction. The data from the 35 and 90 degree detectors were compared in this study. The 90 degree detector spectra, which do not show substantial Doppler shifting, were used as gates to filter out unwanted peaks from the 35 degree spectra. These coincidence matrices were analyzed via the Doppler Shift Attenuation Method (DSAM) and used to calculate lifetimes. Lifetimes of 14 excited states were measured via DSAM, which compares the slowing-down time of 73As nuclei in the target with the decay time of each state of interest. Whenever possible, mean lifetimes were measured by gating from above the transition of interest to eliminate the dependence on unknown side feeding. Quadrupole deformation parameters β2 were inferred from the lifetimes assuming axially-symmetric shapes and compared directly with those from total Routhian surface (TRS) calculations. The trend of the experimental β2 values with spin showed better agreement with the predicted ones for the positive-parity states than the negative-parity states.

Optimal Control of Malaria Across Sub-Saharan Africa Temperature Gradient

Dr. Folashade Agusto, KU Department of Ecology and Evolutionary Biology Ecology and Evolutionary Biology, University of Kansas

In this seminar, I will present the results obtained from investigating the optimal control strategies for malaria in the presence of temperature variation using a temperature dependent malaria model. A 2015 study by Agusto et al. [1] identified the suitable temperature ranges for mosquitoes in four different geographical regions of Sub-Saharan Africa as [22.61 C – 28.58 C] in West African cities, [16.68 C – 27.92 C] in Central African cities, [19.04 C – 26.75 C] in East African cities, and [16.66 C – 25.32 C] in Southern Africa. The optimal control strategies in these temperature ranges suggest on average a high usage of both larviciding and adulticiding followed by a moderate usage of personal protection such as bednet. The average optimal bednet usage mimics the trajectory of the mosquitoes as the mosquitoes respond to temperature variations. These results triggered the investigation of the impact of insecticide resistance mosquitoes on disease burden in the face of temperature variations. The results indicate that optimal bednet usage on average is higher in the presence of insecticide resistance mosquitoes. Furthermore, on average bednet usage increases as temperature increases to the optimal temperature suitable for mosquitoes and it decreases thereafter, a pattern similar to earlier results involving insecticide sensitive mosquitoes.

Modeling COVID-19 Outbreak: A Cross-Species Approach

Lucas Delibas, Bryan Harris and Rylan Sampson, UMKC Math and Stat Department

Just as quickly as COVID-19 has changed the way of living, there is now an intense demand for modeling the disease and predicting its spread. In this presentation we propose a human-animal-environment compartment model quantified by a system of ordinary differential equations in order to model the infection status of the populations of humans and vector animals in the contagion environment at the origin of the pandemic. We will analyse the disease-free and endemic equlibria of our model and offer some suggestions as to prevent the virus’s spread.

News Corporation Spinoff of 21st Century Fox and The New News Corp: An Event Study

Vanessa R. Collins, UMKC School of Business

The spin-off of 21st Century Fox and News Corp from News Corporation had an impact on shareholders’ equity. This research project examines the significance of the spinoff on shareholder value by looking at the stock price. Our study takes the historical value of share prices and compares them to the price when the separation event took place on June 28, 2013. We use regression analysis to determine statistical relevance of the actual stock returns achieved. Then, return estimates are generated to compute stock price deviation from typical return prices. While there was a 5% decrease in returns throughout the event, prices stabilized back to normal growth. Over the time interval of the News Corp spinoff, the average net abnormal return was 0 %. So, shareholders faced a negative impact of value on and around the event date, but over time that negative return leveled out. Other research has shown the positive influence of spinoffs on corporate operations, profitability and stock market performance.

A Mathematical Model for Examining the Effects of Resistant Salmonella in Developing Countries

Matthew Shirley, UMKC Math and Stat Department

Antiseptic procedures and antibiotics eliminate harmful bacteria; however, some bacteria develop resistance. This model examines the spread of two strains of a harmful species, specifically salmonella, within a population of susceptible hosts. The first strain will behave similarly to observed data of salmonella outbreaks. The second strain’s spreading parameters will be modified to reflect an assumed resistance to antiseptic and antibiotic treatments. This study used a double susceptible-infected-recovered-susceptible with free living pathogens growing in the environment. It used the next generation matrix approach to calculate the basic reproduction number, and other methods of analysis to predict the existence of endemic equilibria and their stability. It ran numeric simulations to confirm the predictions. The study shows that conditions can exist whereby an outbreak of mixed strains of the pathogen can result in an endemic equilibrium that resembles the endemic equilibrium of an outbreak with no use of antiseptic or antibiotic measures. In other words, the resistant strain renders ineffective measures intended to contain the outbreak.

A Mathematical Model to Investigate Epidemic Waves of Math Anxiety

Dilek Soysal, Arash Arjmand & Deepak Sireeshan, UMKC Math and Stat Department

Background: This research develops a simple dynamical system framework to study the role of social mechanisms on the prevalence of math anxiety in our entry-level math courses. Math anxiety is the self-reported discomfort when attempting mathematical problems. This feeling prevents students from pursuing careers in science, technology, engineering, and mathematics. Objective: The purpose of this project is to study different possible outcomes that result from the interaction between anxious and non-anxious students. This project has both mathematical goals and potential social goals. Method: In this project, we have considered “anxiety” as a contagious disease and used SIR model to tackle the problem. Results: We have been able to derive the equation for “Basic reproduction number, 𝑅0” which translates to “Theoretical number of people that can be affected by an anxious student”. We have also derived mathematical conditions on parameter that dictates the epidemiological behavior of the system. Conclusion: The main significance of this project is to identify where to intervene throughout the semester to reduce the Drop/Fail/Withdraw rates and reduce the anxiety among the students.

A SEIQR Model to Investigate Travel Dynamics from City of COVID-19 Origin to Rest of World

Kodi Kuhlmann, UMKC Math and Stat Department

The Coronavirus, identified by WHO on January 7th and later officially named COVID-19, began in Wuhan City, Hubei Province of China, and has since spread around the world. Our model focuses on the spread of this contagion from the main airport in Wuhan City to the busy New York subway system. Using a double SEIQR model including travel dynamics, we found a set of ten differential equations that allowed us to study and graph the spread of the coronavirus from the virus origin to a densely populated area closer to home. Our hope is that our results will help show how quarantining and imposing travel restrictions reduce the spread of COVID-19, and thus enforce the idea of “stay-at-home” to help “flatten the curve.” Also, it is our goal to determine whether this outbreak is a onetime occurrence, or if this virus will reoccur every winter, and how devastating the recurrence could be. While we’re still in the process of perfecting our model and wrapping up our research, early results have shown how imposing travel rates greatly reduced the spread of the coronavirus from the virus origin to the New York subway system. We have mixed results on whether the coronavirus will reoccur in future years.

Simulations and Analysis of COVID-19 Spread: Lessens to be learned

Pleasance Mertz, UMKC Math and Stat Department

The COVID-19 novel coronavirus, identified in Wuhan, China in December 2019, has spread to most of the globe. W develop a double SEIQR model designed to predict the transmission of the virus from a city with an outbreak to a city with no infected persons. In particular, we model the spread from Wuhan City to New York City via their main travel hubs, the Wuhan City airport and the New York City subway system. We then analyze the effects of control measures such as travel restriction, quarantine, and self-isolation (“social distancing”) on the course of the spread of the disease, as these are the main methods of control in the absence of vaccines and/or known medicines to prevent or treat the infection. Our model verifies that without adherence to these measures, the virus may not be eradicated and the number of cases will either remain high or fluctuate seasonally. Therefore, travel restrictions, proper quarantine of infected individuals, and strict adherence to self-isolation measures should remain in place in order to gain control of the number of active cases, assuring that health care systems will not be overwhelmed.

Dependence of AGN Activity on Cluster Mass and Cosmological Distance in the SPT Cluster Surveys

Benjamin Floyd, UMKC Physics and Astronomy Department

The number of active galactic nuclei (AGN) in galaxy clusters has been observed to grow by nearly two orders of magnitude looking out from the local universe to ∼ 9.3 billion light-years (ly) away. Star formation rates in clusters have also been observed to rise rapidly over this interval. These trends, along with several other recent observations of distant clusters, have led to the idea that this enhanced star formation and AGN activity may be driven by galaxy mergers within the clusters. Since mergers are more efficient in lower mass clusters with smaller galaxy velocity dispersions, the expectation is that AGN incidence should scale inversely with cluster mass. A recent study using X-ray selected AGN has offered some support for this model in nearby clusters, though with large uncertainties. We select infrared (IR) bright AGN from a large, uniform, mass-selected galaxy cluster sample from the South Pole Telescope spanning a range out to 9.7 billion ly away for which we have acquired follow-up Spitzer Space Telescope observations. With these data we use Bayesian statistical modeling to explore the incidence of IR-bright AGN in clusters as a function of cluster mass, redshift, and projected cluster-centric radius.

Application of Poisson Process for Seismic Ground Simulation and Life-cycle Multi-hazard Bridge Resilience Assessment

Mostafa Badroddin and ZhiQiang Chen School of Computing and Engineering, Civil and Mechanical Engineering Department

Civil structures and infrastructures are required to retain their resilience to both hazardous strikes and progressive degradation over their design life. To achieve such a goal, it is necessary to assess the lifetime resilience of structures subjected to natural hazards and progressive deterioration to reduce the socio-economic effects of structural failure. This study presents a stochastic framework using the Poisson process to model the earthquake occurrence in a lifecycle of a generic bridge system in its 75 years of service, during which time-varying aging-related degradation occurs to the bridge as well. For this purpose, the bounded Gutenberg-Richter recurrence model is used to obtain the earthquake occurrence rates. Time-variant material properties are estimated at the exponentially distributed arrival times of extreme events from the homogeneous Poisson process. To consider the uncertainties corresponding to the capacity degradation due to progressive deterioration, a Monte Carlo simulation based on Latin hypercube sampling is performed and the initiation and propagation of chloride-induced corrosion process are simulated. The damage-based functionality associated with the bridge is modeled based on the integrated local and system-level ductility demands. The research findings in this talk outline how cumulative capacity degradation and sudden extreme events affect the performance of the bridge systems. It is expected that the research framework can assist civil engineers in carrying out objective decision-making over the life-cycle resilience for bridges in seismically active regions.

Modeling and Simulation of Diffraction Through a Circular Aperture

Jeffrey Thomas Harris and Layla Ali M Shafei 

Department of Physics and Astronomy

Electromagnetic plane waves incident on an aperture will always exhibit diffraction to some degree. The resultant diffraction pattern qualities depend on the properties of both the electromagnetic wave and the aperture. Such properties include wavelength, distance from aperture to plane of observation, ratio of wavelength to aperture scale, shape of aperture, and angle of incidence. In this project we have derived diffracting monochromatic plane wave solutions to the Helmholtz partial differential equation by the method of Green’s functions. The solutions are then used to find an intensity distribution on an observation plane as a function of the aforementioned properties of the diffracting wave-aperture system. The intensity distribution was them simulated using Mathematica so as to illustrate how changes in these properties are manifested in the diffraction patterning. Attempts were then made to reproduce these results by passing a plane wave 351nm excimer laser beam through a circular aperture.

Using Sturm-Liouville Theory to Analyze Steady State Schrodinger Wave Equation

Sarah Cole (Mathematics and Statistics), Mohan Gajendran (Civil and Mechanical Engineering), Ronald Morris (Mathematics and Statistics)

Quantum mechanics is concerned with finding a particle’s wave function, which is found by solving the Schrodinger equation. The focus here is on the steady state or time-independent wave equation where velocity is independent of time. There are many specific applications of the time-independent Schrodinger wave equation in quantum mechanics, but the focus here was the Harmonic Oscillator problem with a mass attached to a spring of constant force. We took an analytical and numerical approach to the study of the harmonic oscillation problem. Since this is a special case of a Sturm-Liouville problem, we were able to apply some approaches in SL theory to study this problem from an analytic perspective. The goals of the project were to solve the equation using separation of variables and then go through a series of steps using SL theory to show that the solutions (eigenpairs) take on discrete values only. In our numerical approach, we are confirming results in the paper “Numerical Determination of the Eigenenergies of the Schrodinger Equation in One Dimension” by Hugdal, HG and Berg, P. In the paper, the authors applied finite difference method to the harmonic oscillation problem. Using our own code and knowledge, we modeled the equation using finite difference method to confirm the results of the paper. We also took the paper a step further and used Runge-Kutta 4, and Runge-Kutta 8 to see how well the numerical results approximated the actual and the results given by finite difference method.

Approximate solutions of a projectile equation using perturbation theory

Hope Pleasance Mertz (Mathematics and Statistics), Arman Nokhosteen (Civil and Mechanical Engineering)

In this study, the projectile motion of an object considered to be a concentrated mass has been studied using regular perturbation theory. The approximate solution has been obtained by using various numbers of approximation terms. By non-dimensionalizing the projectile motion equation, analytical solutions based on the number of utilized approximation terms were obtained and subsequently plotted to map out the trajectory of the projectile mass. By adding terms to the equation of motion that consider both the effect of changing gravitational attraction and wind resistance (modelled by using a constant value, K) on the object, the authors were able to show the accuracy of the utilized perturbation method for obtaining an object’s trajectory, described by a fairly complex equation of motion. For validation of the results, a separate solution was achieved by solving the equation of motion numerically using the built in, fifth-order, Runge-Kutta solver in MATLAB. The results show that as the terms used for approximation increase, so does the accuracy of the approximate solution. Furthermore, it is also shown that after a certain number of terms have been used, the accuracy of the results does not continue to increase; therefore, it is possible to truncate the approximate solution for simplicity. In this study, it is shown that by using second order approximation terms, an acceptable level of accuracy can be achieved, and therefore, the approximate solution of the perturbation method is in good agreement with the fully numerical solution obtained from the Runge-Kutta based solver.

Connecting Sturm-Liouville Theory and The Principle of Stationary Action Through Free-Particle Dynamics

E. Hauptmann (Physics and Astronomy) R. Kuhlmann (Mathematics and Statistics)

The principle of stationary action is one of the most important and fundamental concepts in physics. It states that a given physical system will evolve in a way such that the action of the system remains stationary. By applying this principle, one can obtain the equations of motion of a given system. This project recasts the process of finding the equations of motion into a Sturm-Liouville problem. In doing so, restrictions must be applied to the types of systems that can be analyzed using Sturm-Liouville theory. These restrictions, and how they come about, will be shown through applying Sturm-Liouville theory to a free-particle system; a point particle with no forces acting upon it.

A mathematical model to study the effects of partial remediation of groundwater contaminant source

Hussain Jabr B Alantar (Mathematics and Statistics)  Mehmet Uylukcu (Curriculum and Instruction EDSP) 

Globally, groundwater resources have become a threat from growing demands, wasteful use, and contamination increasingly. To encounter this dilemma, proper planning and management practices are needed. To manage groundwater resource, key management is to be to model the movement of fluids and contaminants in the subsurface. The objectives of this project are to understand how the contamination moves in the groundwater by using a mathematical model and to know the concentration and mass rate of change of the contamination in the groundwater over time and distance. In the purpose of preparing such a model, we proposed a real-world model. This model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines. In this study, analytical models for predicting groundwater contamination is isotropic, and homogeneous porous formation is derived. The impact of dispersion and diffusion coefficients is included in the numerical solution of the advection-dispersion equation (ADE) subjected to transient (time-dependent) boundary conditions at the origin. Numerical solution is obtained by using Matlab. Numerical results are obtained to compare between two different chemical substances.

Applications of principal component analysis in multichannel image processing

Babak Poorebrahim Gilkalaye (Electrical and Computer Engineering)

Principle component analysis is widely used to reduce the dimension of the data set, as working with lower dimension data set is more efficient in terms of both time and size. Time complexity of many tools in data science is polynomial or even exponential so avoiding higher dimension data set is crucial. In this project we plan to reduce an image size by using SVD replacing some less important singular values with zeros. We treat an image as a 3d matrix and apply SVD separately on each channel and then all reduced channels are combined again and reconstruct the compressed image. The image size could be reduced up to 50% in this method while the legibility and clearness still are preserved.

Cooperative Values and its Effect on Employee Satisfaction within the Multilevel Structure of Organizations

Vanessa R. Collins (School of Business)

Businesses cannot possibly operate efficiently on a one-way closed system management style. Several online shopping experiences ask for feedback from customers after they have been shopping on the website. In the same way, other businesses and government seek to gain valuable consumer opinions by conducting surveys. The National Partnership for Reinventing Government employee survey was conducted in the early nineties to gather information about employee satisfaction within their government entity employers. The survey was administered to measure the success of government employers through a business model that researches employer-employee relations. The dataset consists of survey responses from 21,257 government employees in the various fields of the United States’ national government. The survey is composed of 32 questions inquiring about employees’ opinion of their working group, office, and its operations.

Within this secondary data analysis, I use the SPSS statistical analysis tool to test my hypotheses statistically with a chi-square test for independence between the responses of two different questions from the government employee survey. In each scenario, I use two of the survey questions as the variables to the hypothesis. I’m seeking to answer the question: What types of employer involvement increase employee satisfaction? Another question that could be answered here is: Is there any consistency between the number of agree responses to one question and the number of agree responses to another question? So, the survey questions were taken as variables and compared against each other to determine whether there is a relationship between questionnaire responses.

Error Analysis of Inline ZFP Compression for Multigrid Methods

Avary Kolasinski (Mathematics Department, University of Kansas)

ZFP is a state-of-the-art lossy compression algorithm that can easily be used inline during numerical simulations due to the inherent locality of the algorithm. Using ZFP fixed-rate mode, which compresses a block to a fixed number of bits, ZFP can be implemented as a new data structure similar to a double precision array. Multigrid methods update the current iterate by approximating the error on coarse grids. Depending on the application, e.g. using multigrid as a preconditioner, the solution using ZFP compressed arrays can significantly reduce the storage cost while maintaining the required accuracy. The information that is lost during ZFP compression may represent the traditional errors however, any additional error caused by ZFP could contaminate the solution. It is important to understand if the error from ZFP compression overwhelms other sources of error. The goal of this talk is to analyze the stability of using ZFP in multigrid methods.  We use previous error bounds to establish a bound for the error for fixed-rate ZFP when used in multigrid methods. Furthermore, we analyze the relative error for an adaptive rate multigrid algorithm.

Illustrating Regression Tree Using Boston Housing Data

Tahani Omer (Mathematics and Statistics)

Regression tree is a commonly used method in data mining. Similar to regression analysis, the goal is creating a model to predict the value of a response from several predictors. In this work, we describe how to generate a regression tree using the decision tree method. This includes how to first build a large tree, how to prune it to find the best sub tree, and how to identify the cost complexity parameter via the cross-validation approach. Then, Regression is employed for the Boston housing data set. I find that the tree indicates the higher percent of lower status of the population, corresponds to less expensive houses.

An agent-based modeling approach to analyze dynamics of Johne’s disease on US dairy farms

Malinee Konboon (Mathematics) 

Using the Netlogo, a sophisticated agent-based disease model is constructed to investigate the dynamics of  Johne’s Disease on US dairy farms. We investigate the incidence and prevalence of the infection under different case scenarios.

Economic Growth, International Trade and Debt: A Model to Understand Developed and Non-Developed Countries

Ariel B. Ibañez-Choque (Economics) 

This paper has the aim of show the effects of external debt and interest debt payments on the rate of economic growth by developed and non-developed economies. Previous papers studied the effect of balance of current account and/or deficit in trade balance on the rate of economic growth. But, surplus in trade balance economies, and their international trade relation with deficit economies, have not been studied sufficiently. So, our innovation is to explain the rate of economic growth in a world economy with two opposed countries in their balance of payments and in their economic structures. In that sense, the results show three mechanisms of dependency between developed and non-developed countries in the international trade: “terms of trade” relation, “interchange real” relation, and “interest debt” relation. In addition, I found that the growing gap of income level between countries is determined by their economic structures, then non-industrialized economies income levels are severely affected by international trade.

Numerical methods for finding eigenvalues of a generalized population matrix

Spencer T. Smith (Mathematics), McCoy Matthew (Mathematics)

The purpose of this project is to use numerical methods for finding eigenvalues of a generalized matrix A for modeling the natural life of a hypothesized beetle as described by Harro Bernardelli’s paper “Population Waves”. The matrix A takes the form of having the death rates from one age group to the next along the lower diagonal, and their birth rates appear in the first row. The group will attempt to generalize the exercises found in \Numerical Analysis” by R. Burden et al. in order to gain a broader understanding of the system outlined there. The main focus of this presentation is to present numerical techniques, such as the power method and Wielandt deflation, to obtain eigenvalues. Eigenvalues are important because they allow researchers to find a \nice” initial population in the sense that A applied to these convenient populations will result in a population of proportional size. That is, we solve the problem Av = tv, where v represents an initial population for different age groups.

Fitting Oxygen Consumption Versus Live Weight of the Larvae of the Moth Pachysphinx Modesta

Azzah Alshekhi (Mathematics), Ying-Yin Chang (Statistics), Abdullah F. Alshuyokh (Mechanical Engineering), Sahib A. Hasan (Physics) 

The project is inspired by the paper “ Energy budget of the larvae of the moth Pachysphinx modesta” (Schroeder 1971), which is about energy budget, where the energy budget equation is given by I =G +E +R, such that: I is the ingestion, G is the growth, E is the egestion, and R is the respiration. The experiment has been done on the larvae of moth of Pachysphinx modesta , beginning from the larvae hatches, and ending when the larvae pupates. The goal is to find the best model that would fit the data given in the paper of Schroeder 1971 of oxygen consuming R and live weight W. We tried a mathematical model, which is the logarithmic linear least squares polynomial model that is given by , and the quadratic as well, and compared the goodnessbWa  of fit with statistical regression models. However, the logarithmic quadratic model is the best fit for the data. The work and the experiment could be extended to cover the whole life-cycle of the moth Pachysphinx modesta.

Using MATLAB to estimate parameters in a mathematical model of hemorrhagic disease

Gerry W. Baygents (Mathematics) 

Hemorrhagic disease (HD) is a significant and fatal virus affecting white-tailed deer in Missouri (and the United States as a whole).  A set of delay differential equations is proposed to model the dynamics of HD.  Parameter values within these equations are estimated using MATLAB using two different techniques.  First, some values are directly estimated using data from the Missouri Department of Conservation using MATLAB’s curve-fitting app. Second, three scripts are written to simulate the remaining parameter values and choose the set of values with the smallest sum-of-square error (SSE). When computationally too demanding or when the results do not reasonably approximate the data, modifications to the model and code are made to derive a final set of values.

A mathematical model to analyze dynamics of free-living bacteria in the environment

Tahani A. Omer (Statisitcs) 

The classic logistic rate equation is a growth model derived from the concept that without significant mortality, a population’s momentary growth rate in a closed habitat is controlled by two major elements; one directly proportional to momentary number of cells present and the other directly proportional to the portion of the remaining unused resources. However, the logistic model does not account for at least some cells mortality that can occur at any time, including during the exponential growth stage. This problem can be eliminated by considering the number of individual in the equation as a number that represents the population’s net growth [1]. Moreover, the logistic model assumed that the growth rate of a population at any time depends on the relative number of individuals at that time. In practice, the process of reproduction is not instantaneous. We can overcome this difficulty by considering the controlling effect depends on the population at the beginning of the experiment [2]. In the present work we will develop a more realistic model which takes advantage of above mentioned modeling approaches and we employ the model to investigate the effects of decontamination on the growth and survival bacteria in the environment.

[1] M. Peleg, M.G. Corradini, M.D. Normand (2007) the logistic (Verhulst) model for sigmoid microbial growth curves revisited food research international 40 (2007) 808-818.

[2] Norman MacDonald (1978) Time lags in Biological Models.

Preliminary modeling for neural network trading algorithms

Daniel A. Shanaberger (Physics), Dhuha F. Shareef (Mathematics) 

We analyze 12 years of daily values of the Dow Jones Industrial Average. We prepare a variety of neural networks to predict ‘next day’ values, and make theoretical trades based on the known opening and closing values. We compare these different models by calculating a ‘goodness of fit’ as well as a ‘goodness of trade’. We test if modeling the input data can improve each network’s predictions.

Probabilistic multi-hazard framework for scour and earthquake effects on bridges

Mostafa Badroddin (Civil Engineering), ZhiQiang Chen (Civil Engineering) 

Many areas of the world are prone to several natural hazards such as flood, earthquake, windstorm, and fire. Therefore, in this study a probabilistic multi-hazard framework is developed to evaluate the structural response of river-crossing bridges under the combined effects of flood-induced scour and earthquakes. For this purpose, nonlinear pushover and time history analyses have been conducted to investigate the effects of foundation scour on seismic performance using a sophisticated finite element based model. In order to take various sources of uncertainties into account, probabilistic framework has been employed. Toward this goal, Incremental Dynamic Analysis using Latin Hypercube sampling has been carried out to consider scour depth, ground motion intensity, and material properties uncertainties. Results implies that foundation scour is a complicated multiphysic phenomenon that may be considered as a beneficial factor towards mitigating seismic force demands.

Exploration of Different Trends of Atmospheric CO2 as Measured From Mauna Loa NOAA/ESRL Observatory

Benjamin T. Floyd (Physics), Zhiheng Zhang (Statistics) 

Global warming is widely considered to be the largest threat to our civilization and environment. Greenhouse gases play a crucial role on affecting the overall warming trend. Carbon dioxide contributes the majority of all greenhouse gasses in the atmosphere providing 64.3% of all the greenhouse gasses produced by humans. Our project attempts to quantify the trend of increasing carbon dioxide concentrations over a sixty-year period. We also examine the seasonality of the data using periodic models. We find that a quadratic trend plus a sum of sine seasonality models the data well according to standard goodness-of-fit measures.

A surface moving mesh method based on equidistribution and alignment

Avary J. Kolasinski (KU Mathematics) 

Given a mesh on a surface, our goal is to improve the quality of the mesh using a moving mesh method. To this goal, we will construct a moving mesh method based on mesh equidistribution and alignment conditions. We will then discuss several proven advantages of this surface moving mesh approach. Finally, we will study various numerical examples.

Incorrect Use of U-Substitution and Application of Residue Theorem to Evaluate Real Integrals

Majid Bani-Yaghoub,
Department of Mathematics & Statistics,
University of Missouri – Kansas City (UMKC)
http://b.web.umkc.edu/baniyaghoubm

This talk is mainly directed towards undergraduate and graduate students, especially those who are considering an academic career. In calculus I, the u-substitution is introduced as a method of evaluating definite and indefinite integrals. The concept of u-substitution will reappear in calculus II, where trigonometric substitutions are discussed. While u-substitution is a powerful method of evaluating integrals, it requires the function to be continuous in the range of the substitute function. This important condition is often missed in classroom instructions, which may cause issues for evaluating trigonometric integrals. In this talk I provide a few examples, where incorrect use of u-substitution leads to miscalculations of definite integrals. Then I employ alternative methods such as residue theorem to obtain the correct solutions.

Modeling the Dynamics of HIV Infection in the Brain

Colin Barker

UMKC Graduate Teaching Asisitant
MSGSO President

Throughout the last 30 years Human Immunodeficiency Virus (HIV-1) has been an international epidemic. It is known that HIV-1 exists in the bloodstream as well as several locales in the body that act as reservoirs, in particular the brain. Highly Active Antiretroviral Therapy (HAART) has proven effective at causing the virus within the bloodstream to subside, however, the Blood-Brain Barrier (BBB) prevents most HAART drugs from penetrating into the brain. Huang, Zhang, et al just recently presented a model illustrating HIV persistence through the network of lymphocyte recirculation–perhaps the first model of its kind. We introduce a novel model incorporating uninfected susceptible cells inside the brain. Our model accurately predicts virions in the brain, and suggests that infection in the brain persists and may cause reinfection of HIV-1 within the bloodstream.

Using movement cattle data and Markov epidemiological models to quantify the dynamics of Johne’s disease in dairy farms

Jacob L. Pennington
UMKC Master’s Student

On a typical dairy farm, cattle are separated into pens, grouped with cattle in similar life stages. Cattle are moved between pens as they transition between stages. These movements can impact on how a disease may spread through a farm. The objective of this study was to analyze data collected showing the location of cows within several real-life farms to discern a Markov-chain to effectively model the transitions of cattle between the pens as well as modeling the progress of infection within individual subjects to simulate the spread of infection through a farm. By varying aspects of each of these Markov chains, the simulation can further be used to examine the impact of control methods on the progress of the disease.

Using a computational package in R, transition probability matrices were derived for each farm within close tolerances. Then, a number of trials of simulations were run that demonstrated quantitative differences between the progressions of the disease depending on the farm. Simulations were also run using a control method -the “test and cull” method- which showed a qualitative difference versus applying no control methods.

These methods lay a groundwork that could be used as a Markov Decision Process to not only test and compare various control methods, but to also optimize when each control method is best applied in order to maximize the probability of the farm.

Predicting the Effects of Control Policies for Johne’s Disease Using Mathematical Modeling

Taylor D. Little
UMKC Math Major

Each year, US dairy farms lose millions of dollars due to Johne ’s disease. Many measures exist to help stifle the disease, yet the current project focused on three different measures in order to simplify the model and focus on efficacy of said measures. Using a mathematical modeling approach, the goal of this project was to simulate multiple combinations of disease-suppressing strategies to determine the efficacy of control and preventive policies.
The model was built using two others as a base for what we wanted to create: We wanted a new model that focused on age and disease progression simultaneously, instead of putting emphasis on just one of these variables. We also added an “environment” variable that is not present in one of the more reliable models already in existence. There were three different policies that were considered for prevention of disease spread. The first was “limiting animal contacts” meaning putting a limit on how cows sharing an environment. Second policy was “test and cull”, which uses one of the current tests available in order to identify those infected, and then removing those infected from the farm. Lastly, we wanted to test for a more aggressive “environmental decontamination” policy; by this, we mean cleaning the pen environments through power wash and scraping more frequently.
Simulations of the model meant first creating equations that would represent each stage of age and disease progression in the model. Using a Matlab solver program, we plugged in these variables and equations, which then simulated these measures. Graphs of the solution curves and the prevalence were then obtained by running the Matlab program, which allowed us to see the results.
It is important to note that we found the results were dependent on the time frame in which we ran the model. The policies had very different outcomes based on short-term (5 years) and long-term (20 years) periods of intervention. While “limiting animal contacts” and “environmental decontamination” were more effective in 5 years intervals, their long-term effects significantly diminish. On the contrary, “test and cull” was more effective in long-term intervention applied to calf and adult populations, but it was not significant in the heifer population. Combining 2 of the 3 measures allowed for even better results, although it is important to note that combining all 3 methods did not show a significant change. The most effective results was a combination of testing and culling and limiting contacts.

Multi-patch modeling and analysis of hemorrhagic diseases in Missouri’s white-tailed deer 

Gerry W. Baygents,

UMKC PhD Student,

Epizootic hemorrhagic disease and bluetongue are two orbivirus-related diseases (HD) of white-tailed deer with multiple outbreaks in late July through November are spread by the small biting midge, Culicoides Ceratopogonidae. HD outbreak is a major concern in the wildlife and natural resource management, and using mathematical modeling, we explore efficacy of various control strategies. In particular, an epidemic model is proposed to analyze the HD dynamics between multiple patches due to deer population dispersal. The model embodies deer movements between the patches and the vector-borne infections within the patches. In the present work (1) using the harvest, disease mortality and dispersal data of deer population in Missouri, the host-related parameter values of the model are estimated, (2) the conditions for existence and stability of equilibria are established, and (3) the local and global basic reproduction numbers are respectively calculated for each patch and the entire environment. It is shown that increasing movements of susceptible deer from patches with reproduction numbers greater than one to those with reproduction number less than one can only be an effective control strategy when it is combined with suppression of the midges’ population in all patches.

Context Set Weighting Method

Hee Sun Kim
Department of Mathematics,
University of Kansas

Finitely-valued time series are described by the conditional probabilities of the possible values given the infinite pasts. The relevant values in the infinite pasts that determine these transition probabilities are called contexts. The context is generalized to be a not necessarily consecutive sequence of values. The collection of the contexts for all possible pasts describes the memory structure of a time series and is called context set model. The context set model parametrized with the transition probabilities determines the likelihood for a sample.
For time series with unknown context set models, statistical estimation of the likelihood from a sample is considered with the requirement that the sum of the estimated likelihood over all possible length-n samples is one. The presented Context Set Weighting method uses a double mixture over all possible context set models and the set of parameters of each model. The CSW method is shown to minimize the worst-case difference between the logarithm of the estimated and the true likelihoods. For a sample the number of possible context set models is large, but it is shown that the method can be computed in polynomial time.
The above statistical problem is motivated by information theory. Information sources with finite alphabets are modeled by finitely-valued processes. Lossless codes of messages can be constructed from probability distributions over the length-n samples. The CSW method provides a code with minimum worst-case code length. Thus, the CSW method can be applied to construct a universal code for class of context set models.

Modeling Effects of Morphine Pharmacodynamics on Antibody Responses and HIV dynamics

Jones Mutune Mutua,
UMKC PhD Student

Drugs of abuse, such as opiates, have been widely associated with enhancing HIV replication, accelerating disease progression and diminishing host immune responses, thereby making it harder to effectively manage HIV infections. Here, we develop a mathematical model that incorporates the pharmacodynamic properties of morphine which may alter antibody responses causing adverse effects on HIV dynamics. We analyze our model to study how periodic morphine intake affects HIV infection.

Wear Model of a 2D Axisymmetric Mechanical System with Friction

Dr. Dell Elhomani
Department of Electrical and Computer Engineering

The aim of this paper is to further enhance the assumption made by Elhomani and Farhang [1] in their 2D axisymmetric thermal lumped parameter model of a braking system in dry friction; in which they assumed that asperities in contacts burst after they reach the threshold temperature of 2000 °C. The wear model developed in this paper examines their assumption by predicting the mean time between the time asperities engage in contacts and the time they wear out; in other words, the mean time during which asperities remain in contacts throughout a braking scenario of a carbon-carbon composite disk pair in dry friction contact. Also a formulation of the probability density functions of asperities-in-contacts and asperities-wearingout have been formulated.

Spatial and spatio-temporal cluster analysis of hemorrhagic disease in Missouri’s white-tailed deer population

Gerry Baygents
Department of Mathematics and Statistics

Hemorrhagic disease (HD) is the general term for two diseases with similar characteristics and symptoms, epizootic hemorrhagic disease and the bluetongue virus. The disease is spread by the small biting midge, Culicoides Ceratopogonidae. Using data from the Missouri Department of Conservation, I will determine if HD in Missouri’s white-tailed deer occurs in space or in space-time clusters. Using a Martin Kulldorff’s program SaTScan – and its corresponding scan statistic – I will use three approaches to detect potential HD clusters. These results will be used to predict patterns in outbreaks. Because of several unknowns associated with HD, it has been widely considered to be uncontrollable in wildlife. Being able to predict years of higher-than-average outbreaks may enable conservationists to take precautionary steps to control the disease.

A hybrid modeling approach to study the dynamics of Johne’s disease in dairy farms

Malinee Konboon
Department of Mathematics and Statistics

I will be explaining our work with modeling Johne’s disease in dairy cattle. This fatal disease is incurable and causes considerable economic losses to the industry. We have implemented a hybrid modeling approach to study the effect of cattle movement patterns on the spread of disease. Using the hybrid model and the movement data of two dairy farms and we have derived recommendations to reduce the infection risk in each pen through optimal management of cattle movement.

Modeling Effects of Drugs of Abuse on HIV-Infection Threshold and HIV- Specific Antibody Responses

Jones M. Mutua
Department of Mathematics and Statistics

The frequent use of drugs of abuse among HIV infected individuals is rapidly increasing, and thus, is a major concern in HIV infections. Drugs of abuse enhance HIV replication and diminish host immune responses, thereby making it harder to effectively manage infections. Here, we present a mathematical model that helps quantify the effects of drugs of abuse on altering HIV-specific antibody responses, and analyze the HIV-infection threshold dynamics (Ri). Using our model, we show how altered HIV-specific antibody responses due to drugs of abuse affect viral infection and clearance, viral load, CD4+ T cell count, and CD4+ T cell loss in HIV-infected drug abusers. We find that drugs of abuse such as morphine enhance HIV infectivity and lower virus neutralization among drug users.

Some approaches for statistical process control chart patterns recognition

Dr. Dell Elhomani
Department of Electrical and Computer Engineering

Fast and accurate recognition of the Statistical Process Control Chart Patterns (SPCCP) is significant for supervising manufacturing processes to accomplish better control and to make high value products. SPCCP can display eight kinds of patterns: normal, stratification, systematic, increasing trend, decreasing trend, up shift, down shift and cyclic. With the exception of the natural pattern, all other patterns indicate that the supervised manufacturing process is not performing properly and actions need to be taken to correct the problems. This paper proposes new approaches, neural networks and neural-fuzzy systems, to the (SPCCP) recognition. This work also investigates the use of features extracted from statistical analysis for simple patterns, and wavelet analysis for concurrent patterns as the components of the input vectors. Results based on simulated data show that the proposed approaches perform better than conventional approaches. Our work concluded that the extracted features improve the performance of the proposed recognizer systems.

Regression Analysis of Contribution of Different Industries to the Local Gross Domestic Product for Kansas City, MO

Bader Alanazi
Department of Mathematics and Statistics

Multiple regression analysis is an important statistical technique for studying and analyzing the relationship between a response and a group of predictor variables. In this project, we apply multiple linear regression analysis in an examination of the relationship among the local Gross Domestic Product (GDP) Indices for construction and other industries in the Kansas City, MO metropolitan area.

Lifestyle Impact on Mathematics Performance among Portuguese Students

Rachael Nassimbwa
Department of Mathematics and Statistics

This project is focused on examining the performance of 382 Portuguese students in a Mathematics course (on a scale of 1-20) based on 10 predictor variables (both categorical and quantitative). The analysis is carried out using a multiple linear regression model. The categorical predictors are sex, internet access, whether or not the student is in a relationship, workday alcohol consumption, weekend alcohol consumption, and the health of the student. The quantitative predictors are age, study time, free time, and the number of absences from class. Multicollinearity is examined among the quantitative predictors. In my analysis, I discover that only 4 predictor contribute significantly to the performance of the 382 Portuguese students. This conclusion is reached through the use of Analysis of Variance and via the Stepwise Approach of Backward Elimination. I will also show how the regression coefficients are derived mathematically and provide an examination of the properties of their estimators.

Examining the Relationship among the Annual Prices of Various Metals

Hao Zhou
Department of Mathematics and Statistics

The goal of this study is to examine the relationship among the annual prices of different metals over a period of 100 years. In the first part of the study, metal prices are detrended, and then the linear relationship among the detrended prices is examined. In the second part, a time series model is constructed to model the relationship over time. Several versions of the ARIMA model are constructed, and the best model among the group of constructed models is used to represent this relationship. Several properties of parameter estimators are examined, including the bias, variability, sufficiency, and consistency of each one.

The first statement of the formula for the Normal Curve

Andres F. Cantillo, Department of Economics

De Moivre’s book “The Doctrine of Chances” (2) is thorough account of what was known about probability and annuities. The proof that is the object of this paper is included in the very last pages of the book (pages 235-243). The aim of the present paper is to explicate De Moivre’s first part of the proof in such a way that we can trace back the reasoning behind this creation has shaped the modern way of doing science.

A Measuring Argument for Finite Groups

Joseph M. Leroy, Department of Mathematics and Statistics

Studying the structure of groups is a large field, and counting formulas help in understanding the structure of groups.  We will look at an important counting argument that can be used toward this end. 

Prediction for the Percentage Score in an Introductory Math Course of Freshmen at a University in the Southwestern United States

Xing Xia, Department of Mathematics and Statistics

This study has shown the model of prediction about the percentage score and the corresponding letter grade based on four factors: Gender, High School GPA, Entrance Examination Score, and Race. The study is based on grade data for a certain academic year from over 810 students enrolled in an introductory math course. Success was defined as obtaining a B or higher grade in this course.

Using data from a first-year introductory math course, it was found that the white, female students outperformed other subgroup students. The entrance examination score had the biggest correlation to the overall percentage earned in the course. That makes entrance examination scores a very important factor to consider when admitting students that are entering the undergraduate program, even more important than high school GPA. 

A Mathematical Model of Oral Probiotic and Indigenous Bacterial Ecology Within the Canine Digestive Tract

Tyler W. Brown, Department of Mechanical Engineering

The focus of our research was to mathematically and numerically analyze the effects of probiotic supplementation when administered to dogs.  We took data previously collected by Texas A&M Veterinary School and analyzed it to see how oral probiotics affected indigenous bacterial cultures and vice versa.  Our original model was derived from the Lotka-Volterra competition model, but it was modified to take into account for the probiotic administration. Using the linear stability analysis of the model, we established the conditions for the coexistence of the probiotic with other bacteria native to the gut.  This also yielded the finding that coexistence during supplementation can be achieved in either node or spiral form.  By fitting the model to the data we calculated the changes in the level of competition during, before and after the probiotic administration. Our results confirmed prior studies which show that once probiotic supplementation is discontinued, the probiotic population within the digestive tract diminishes. 

The Problem of Points

Andres F. Cantillo, Department of Economics

According to Katz some of the basic notions of probability existed in ancient civilizations. In The Talmud and in Roman calculations of annuities there is some evidence of this. However, no record of numerical probability calculations exists. Hald, Bernstein and Katz agree that this numerical development was intimately linked to the study of gambling, contracts and profits. These authors also coincide in that the formulation of “The Problem of Points” is a crucial event. The paper is centered on evaluating and explaining the history of the formulation of “The Problem of Points”. The solution to this problem originated the deductive notions of probability. I will center my attention on the formulation and attempt of solution by Pacioli, Cardano, Tartaglia and Forestani. In this process Cardano began to unveil some principles that are coherent with a modern theory of probability.

Time Series Analysis for SandP 500

 Mansour Alghamdi, Department of Mathematics and Statistics

We use time series analysis to give information about an American stock market index and predict the index values in future. The presentation contains basic statistical inference about mean, variance, skewness and Kurtosis. We employ different time series models  such as AR, MA, ARMA, ARCH, ARCH, GARCH and APARCH models and we conduct Model selection via AIC and BIC.

Apple Stock Price Model Building and Forecasting Using Time Series Analysis

Kamel A. Alanazi, Department of Mathematics and Statistics

Time series analysis is the most common method of stock price forecasting, so we use it to perform this mission. We get Apple stock price data from Yahoo finance website. We present summary statistics of log returns, and related statistical inference. We estimate different time series model such as AR, MR, ARMA, ARCH, GARCH, and APARCH and use AIC and BIC for model selection.

Ideal Treatments for HIV-TB Co-Infected populations: Modeling and Optimal Control Theory Perspectives

Abhishek Mallela, Department of Mathematics and Statistics

HIV­TB co­infected individuals undergoing TB treatment often face the dilemma of initiating HIV treatment either immediately or after the TB treatment course is complete. Initiating HIV treatment early during the TB treatment course has advantages such as fewer AIDS­related deaths and a lower risk of HIV transmission as well as disadvantages such as Immune Reconstitution Inflammatory Syndrome (IRIS) and complications arising from a high pill burden. Here, we develop a mathematical model to explore the effects of early and late HIV treatment initiation on new HIV infections, AIDS-related deaths, and new IRIS cases/complications. We identify that the minimum burden that can be achieved with these treatments depends on both the strength and the timing of initiation of HIV treatment. Thus, we also formulate an optimal control problem based on our model, and determine ideal HIV­TB treatment protocols for these co­infected populations.

Dynamics of Hemorrhagic disease in Missouri white-tailed deer population

Evan M. Kraviec, Department of Mathematics and Statistics

Hemorrhagic disease (HD) is primarily transmitted by a biting midge in the genus Culicoides. Over the past 30 years, there have been four major HD outbreaks in the population of white-tailed deer residing in Missouri. We construct a mathematical model consisting of two Susceptible-Infected sub-models, which represent the disease dynamics in deer and midge populations. Using the mathematical model we study the HD outbreaks and make recommendations to reduce and control HD in Missouri. Specifically, the numerical simulations of the model indicate that reducing the contact between midges and deer can significantly decrease the prevalence of HD. The linear stability analysis of the model provides the specific conditions for possible eradication of HD in the Missouri white-tailed deer population. 

Seasonal Dynamics of Hemorrhagic disease in Missouri white-tailed deer population

David Joung, Department of Mathematics and Statistics

Hemorrhagic disease (HD) is primarily transmitted by a biting midge in the genus Culicoides. We construct a mathematical model consisting of two Susceptible-Infected sub-models, which represent the disease dynamics in deer and midges populations. With population of midges grows as temperature rises and during winter they are in their pupa form which stays in the water, so we decided to use seasonal forcing in our model. By adding seasonal forcing term on number of birth of midges throughout the years and run simulations, we have better understanding on seasonal effect on HD and how to reduce the contact between midges and deer by decrease the population of midges. 

Simulating contact mechanics of an anatomical elbow joint

Munsur Rahman, Department of Mechanical Engineering

The elbow joint, recognized as the most important joint of the upper extremity serves as a fulcrum for the forearm. However, this important joint is the most commonly dislocated joint for children and second most commonly dislocated joint for adults. Computational musculoskeletal models of the elbow joint that are capable of simultaneous and accurate predictions of muscle and ligament forces, along with cartilage contact mechanics can be an immensely useful tool in clinical practice. As a step towards producing a musculoskeletal model, the goal of our current research is to develop a subject-specific multibody models of the elbow joint that represent humerus cartilage as discrete rigid bodies that interact with the radius and ulna cartilages through deformable contacts. The contact parameters of the compliant contact law were derived using simplified elastic foundation contact theory. The models were then validated by placing the model in a virtual mechanical tester for a motion profile similar to a cadaver experiment, and the resulting kinematics were compared. The maximum RMS error between the predicted and measured kinematics during the complete testing cycle was 2.7mm medial-lateral translation and 5.50 varus-valgus rotation of radius relative to humerus. After the successful model validation, lateral ulnar collateral ligament (LUCL) deficient conditions were simulated and, contact pressures and kinematics were compared to the intact elbow model. A significant difference in medial-lateral displacement and varus-valgus rotation were observed for LUCL deficient condition. A small difference in contact area and contact magnitude were also observed for LUCL deficiency in the model.