MS07 - ECOP-07

Exploring Heterogeneity in Mathematical Models: Methods, Applications, and Insights (Part 1)

Thursday, July 17 at 4:00pm

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Note: this minisymposia has multiple sessions. The other sessions are: Part-2, and Part-3.

Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Description:

This minisymposium will focus on the mathematical modeling of heterogeneity across various biological systems. Heterogeneity often plays a critical role in shaping the dynamics and outcomes of biological processes. The session aims to: (i) Showcase advances in modeling techniques that capture heterogeneity; (ii) Explore the impact of heterogeneity on predictions and control strategies; (iii) Highlight applications spanning population dynamics, epidemiology, ecology and evolution; (iv) Encourage discussions on the integration of data-driven and theoretical approaches to address heterogeneity. We have confirmed 10 speakers, with 2 more awaiting confirmation (one pending administrative approval at the CDC). Among the confirmed speakers, half are female, and over half are junior researchers, including 1 PhD student and 2 postdocs. Please note that we are going to submit another proposal for the total of 12 speakers.

Tingting Tang

San Diego State University

"Exploring the impact of household size on COVID-19 with coupled SEAIR mode"

During the COVID pandemic, studies have found increasing evidence indicating indoor transmission is very significant and secondary infection rate from household transmission is high. Heterogeneity of transmission among different household has shown higher contact frequency contribute to higher transmission. In this talk, we study the role of household size in the spreading of the virus by developing a coupled SEAIR model. The reproduction number is calculated analytically under simplified condition. Global sensitivity study shows that the contact frequency among family members has high impact on the basic reproduction number, peak infection time and volume. In comparison, quarantined effectiveness from large or small household has little implications.

Collin Kilmer

University of Tennessee at Chattanooga

"Modeling Zoonotic Disease Transmission Under the Impact of Land Use Change"

Land conversion is occurring worldwide due to a growing population and expanding economy. This process increases the likelihood of pathogen spillover, posing significant economic and public health risks. The objective of this presentation is to investigate pathogen spillover from three distinct reservoir species to humans under the impact of land use change. Our models introduce a land conversion index to capture the dependence of the carrying capacity and death rate of wildlife on the proportion of converted land. This index is then used to examine how different levels of land conversion influence pathogen spillover. This is a joint work with Prof. Xiunan Wang at the University of Tennessee at Chattanooga.

Han Lu

University of Alberta

"Analysis of a diffusive host-pathogen epidemic model with two-stage mechanism in a spatially heterogeneous environment"

Due to the spatial heterogeneity present in many aspects of disease transmission, the rate of transmission of infectious diseases, human birth/mortality rate, and the mobility ability of infected humans should be different in different geographical locations. On the other hand, infected humans may exhibit distinct differences in symptoms during the different stages of the disease transmission. This paper aims to study threshold dynamics of a reaction-diffusion host-pathogen model governed by two-stage mechanism and no flux boundary condition. By carrying out strict analysis, the paper establishes the threshold-type results with the basic reproduction number. Specifically, in a homogeneous case that all parameters are constants, we establish the global attractivity of the endemic equilibrium. Our numerical results validate the theoretical results and indicate the importance of the infected humans in the second stage and pathogens in the environment in disease transmission, which greatly contribute to disease spread in a bounded domain and should not be ignored.

Sameras Pal

University of Kalyani, India

"The impact of microbial diseases of corals under macroalgal toxicity, overfishing and rising sea surface temperature (SST)"

Competition between macroalgae and corals for occupying the available space in sea bed is an important ecological process underlying coral-reef dynamic. We investigate coral-macroalgal phase shift in presence of macroalgal allelopathy and microbial infection on corals by means of an eco-epidemiological model under the assumption that the transmission of infection occurs through both contagious and non-contagious pathways. We also investigate coral-macroalgal phase shift in presence of elevated SST and macroalgal toxicity. We found that the system is capable of exhibiting the existence of two stable configurations by saddle-node bifurcations.

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Annual Meeting for the Society for Mathematical Biology, 2025.