MiniSymposium-5: Infectious Disease Modeling and COVID-19 Pandemic: Prediction, Vaccination, Control and Ongoing Challenges


Fola B. Agusto, University of Kansas
Majid Bani-Yaghoub, University of Missouri-Kansas City


Saturday, October 2, 2021 at 10:20 – 11:40 am (CST) (Session 1)


Majid Bani-Yaghoub
University of Missouri-Kansas City
10:20 am

A New Methodology to Decompose Multiple Epidemic Waves of Infectious Diseases Tested by US COVID-19 Data

Mathematical models are useful for analyzing dynamics of infection transmission and estimating threshold quantities such as basic and target reproduction numbers. These quantities can be used to determine the minimum efforts required to eradicate the infection. Despite undoubtable benefits of infectious disease modeling, most existing disease models only support single-peak outbreak dynamics. The present work attempts to fill this gap by developing a theoretical framework for modeling multiple waves of infection. We construct a Summative Susceptible Infected Recovered (S-SIR) model for decomposing the epidemic waves of infection. Using US COVID-19 data the S-SIR model can accurately determine multiple waves of infection, where each wave is characterized with a transmission rate, a growth rate and a carrying capacity. We test accuracy of the model by selecting different time periods of Corvid 19 pandemic in the US. These preliminary results can be used as a guide for future efforts to unpack the heterogenous temporal, spatial and social factors resulting multiple epidemic waves of infectious diseases.

Raul Saenz
University of Kansas
10:40 am

Exploring the Impact of the Spread of COVID-19 on Mental Health

At the start of the COVID-19 pandemic, many states opted for lockdown procedures that left certain populations of individuals feeling anxious and isolated. At the same time, researchers realized the potential of such a unique set of events and began issuing surveys to ascertain how the combination of these factors was affecting the population at large. In this study, we used the COVID-19 Trends and Impact survey to assess possible relationships between COVID-19 cases and deaths, lockdown procedures in each state, and mental health. Understanding how the combination of these factors affects mental health at the population level is crucial for better implementation of lockdown procedures as the pandemic continues to spread. Indicators related to mental health were used as dependent variables while COVID-19 cases and deaths and lockdown procedures in each state were used as independent variables and model selection was carried out using Bayesian Information Criterion (BIC). Initial results of this state-by-state analysis indicate that individual’s mental health was impacted in highly heterogeneous ways. This is joint work with Alexander Fulk, Hiroko Kobayashi, Daniel Romero-Alvarez and Folashade Agusto.

Jordan Bramble
University of Kansas
11:00 am

Stochastic Modeling of Event-Based SARS-CoV-2 Superspreading

The novel coronavirus SARS-CoV-2 emerged in China’s Hubei province in the winter of 2019 and subsequently spread throughout the world, causing over 180 million cases and 3 million deaths to-date. However, SARS-CoV-2 outbreak profiles vary by region. Superspreading – both individual- and event-based – spurs SARS-CoV-2 spread and may contribute to variability. While individual-based superspreading involves individuals who cause disproportionately more infections over their infectious lifetime, event-based superspreading involves public events and/or social gatherings that result in multiple infections. Here, we adopt an event-based framework. Superspreading events (SSEs) are incorporated into a continuous-time Markov chain model in such a way that their influence on outbreak dynamics may be investigated relative to that of non-SSEs. The model further incorporates heterogeneities in transmission from and recovery of asymptomatic versus symptomatic individuals. We explore three versions of this model – two with hospitalization and quarantine and one without – by varying the SSE-related and non-SSE-related infection rates and find that SSE-dominated outbreaks are more variable than non-SSE-dominated outbreaks. This variability has important public-health implications, as it limits prediction robustness and complicates management strategies. These implications suggest a heightened need for targeted control of SSEs. This is joint work with Alexander Fulk, Raul Saenz, Daniel Romero-Alvarez and Folashade Agusto.

Sunday, October 3, 2021 at 11:00 am – 12:20 pm (CST) (Session 2)


Folashade Agusto
University of Kansas
11:00 am

Fire on the Mountain: Modeling the Effects of Prescribed Fire on Lyme Disease

Tick-borne illnesses are trending upward and are increasing source of risks to people’s health in the United States, and there is range expansion in tick habitats due to climate change. Thus, it is imperative to find a practical and cost-efficient way of managing tick populations. Prescribed burns are a common form of land management, it can be cost efficiency if properly managed and can be applied across large amounts of land. In this seminar, I will present a compartmental model for ticks carrying Lyme disease using an impulsive system, and then investigate the effect of prescribed fire intensity and the duration between burns. Our study found that fire intensity has a larger impact in reducing tick population than frequency between burns. Furthermore, burning at high intensity is preferable to burning at low intensity whenever possible, although high intensity burns may be unrealistic due to environmental factors. Annual burns resulted in the most significant reduction of infectious nymphs, which are the primary carriers of Lyme disease.

Alexander Fulk
University of Kansas
11:20 am

Investigating the Effect of Prescribed Fire on the Spatial Prevalence of Ticks

Lyme disease is one of the most prominent vector-borne diseases in the United States and prevalence of the disease has been steadily increasing over the past several decades due to several factors, including climate change. Several methods for control of the disease have been considered, but the effectiveness of one method, prescribed burning, has been hotly debated for well over a decade. In order to provide further clarity on the long-term effects of prescribed burns on the abundance of ticks, we developed a spatial stage-structured tick-host model with an impulsive differential equations system to simulate the effect that controlled burning has on tick populations. Results indicate that while ticks can recover relatively quickly following a burn, frequent, long-term prescribed burns can reduce the prevalence of ticks in and around the area that is burned. We also explored the use of prescribed burns in preventing the establishment of ticks into new areas. A single burn was very ineffective at preventing establishment, but frequent burning can slow and possibly prevent establishment. Finally, a proof of existence of a travelling wave solution to our system was performed. This is joint work with Weizhang Huang and Folashade Agusto.

Dilek Soysal
University of Missouri-Kansas City
11:40 am

Epidemic waves of Math Anxiety Modeled by A system of Ordinary Differential Equations

There is evidence that math anxiety is contagious. In the recent years, there have been attempts to apply the concepts of infectious disease modeling for analyzing spread of math anxiety between the students. Using a compartmental modeling approach, we study the epidemic waves math anxiety occurring prior to midterm and final exams. Our theoretical results coincide with the concept of periodic waves arising from the Hopf bifurcation. This study can be further developed to parametrize the developed model using the available survey data of calculus students.

Key Words: Math Anxiety, Compartmental Model, Hopf Bifurcation, Epidemic Waves

ACKNOWLEDGEMENT: The authors would like to acknowledge the work and comments of Mr. Arash Arjmand and Deepak Sireeshan.

Xueying Wang
Washington State University
12:00 pm

Impact of Varying Community Networks on Disease Invasion

We consider the spread of an infectious disease in a heterogeneous environment modeled as a network of patches. We focus on the invisibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, R0, and study how changes in the network structure affect the value of R0. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in R0. We develop both combinatorial and matrix analytic techniques, and we illustrate our theoretical results by simulations with the exact R0.