MS08 - MEPI-02

Modeling Complex Dynamics in Biological Processes: From Cellular Mechanics to Population-Level Dynamics (Part 1)

Friday, July 18 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Folashade B. Agusto (University of Kansas), Chidozie Williams Chukwu

Description:

Summary: The study of complex biological systems requires a multi-faceted approach that integrates mathematical modeling and dynamical systems across scales. This mini symposium highlights innovative approaches that leverage dynamical systems and multi-scale models to address critical challenges in biology and public health. By spanning cellular, pathogen, and population-level dynamics, this mini-symposium aims to highlight the power of mathematical tools to uncover critical insights and inform strategies for addressing pressing challenges in health and disease. This mini symposium fosters interdisciplinary dialogue, emphasizing the transformative potential of mathematical biology in tackling real-world problems in public health an. Audience: This session will be of interest to mathematicians, ecologists, and biologists interested in modeling communicable and non-communicable diseases.

Blessing Emerenini

Rochester Institute of Technology, USA

"Integrative Triple Therapy Against Bacterial Infections: Exploring Synergistic Dynamics"

Due to their adaptive resistance mechanisms against phages, immune responses, and antibiotics, bacterial biofilms pose considerable challenges to effective treatment, necessitating the development of innovative therapeutic strategies. In this work, we present a comprehensive triple combination therapy model that integrates bacteriophages, innate immune responses, and antibiotics within a highly nonlinear, deterministic, and spatiotemporal mathematical framework. We investigate a range of clinically relevant parameters, including antibiotic dosage and timing, phage administration strategies, and immune response intensity. The formulated model provides mechanistic insights into phage-bacteria dynamics, elucidates post-treatment biofilm structures, and informs precision treatment strategies, particularly for clinically accessible biofilm infections. By bridging clinical applications with advanced mathematical modeling, this work contributes to the development of more effective therapeutic interventions.

Olusegun Otunuga

Augusta University, USA

"Stochastic Modeling and First-Passage-Time Analysis of Oncological Time Metrics with Dynamic Tumor Barriers"

The first-passage-time (FPT) that a tumor size reaches a particular barrier is important in evaluating the efficacy of anti-cancer therapies and understanding certain oncological time occurrences. For certain verified stochastic models describing the volume of a tumor, a moving barrier for the tumor size in which an explicit solution of an FPT probability density function (PDF) exists for the first time the tumor size reaches the moving barrier is obtained in this work. The stochastic tumor dynamics incorporate anti-cancer therapies/treatments that are administered at varying rates. The first-passage-time density (FPTD) is derived and utilized to determine the time at which the tumor volume first reaches the moving barrier, providing a framework for analyzing various oncological time metrics. These metrics include key time measurements used to characterize tumor progression, evaluate treatment response, and capture recurrence patterns in cancer dynamics. The treatment effort needed to cause reduction in tumor size is also obtained. This work is applied to experimental data including the Murine Lewis Lung Carcinoma cells originally derived from a spontaneous tumor in twenty control mice. The time at which the volume of the tumor of each mouse doubles in size is estimated using the results obtained in this study.

Nourridine Siewe

Rochester Institute of Technology, USA

"A mathematical model of obesity-induced type 2 diabetes and efficacy of anti-diabetic weight reducing drug"

The dominant paradigm for modeling the obesity-induced T2DM (type 2 diabetes mellitus) today focuses on glucose and insulin regulatory systems, diabetes pathways, and diagnostic test evaluations. The problem with this approach is that it is not possible to explicitly account for the glucose transport mechanism from the blood to the liver, where the glucose is stored, and from the liver to the blood. This makes it inaccurate, if not incorrect, to properly model the concentration of glucose in the blood in comparison to actual glycated hemoglobin (A1C) test results. In this paper, we develop a mathematical model of glucose dynamics by a system of ODEs. The model includes the mechanism of glucose transport from the blood to the liver, and from the liver to the blood, and explains how obesity is likely to lead to T2DM. We use the model to evaluate the efficacy of an anti-T2DM drug that also reduces weight.

Joan Ponce

University of Arizona, USA

"Impact of DARC Polymorphism on P. vivax Transmission Dynamics"

The malarial parasite emph{Plasmodium vivax} has co-evolved with human populations for millennia. Genetic variants such as the FY(^*)O allele in the Duffy Antigen Receptor for Chemokines (DARC) and the sickle cell allele (HbS) have been naturally selected in malaria-endemic regions because they confer partial resistance to infection, enhancing the survival and reproductive success of carriers. As protective alleles rise in frequency, malaria incidence declines, reducing the selective pressure for further resistance. In this work, we develop a seasonally forced model that couples malaria transmission dynamics with the evolution of DARC genotype frequencies, using fast-slow analysis to capture the multiscale nature of these processes. We derive the basic reproduction number (R_0) and interpret it as a weighted sum of contributions from infected individuals of each genotype. Using data from the Amazonas region of Brazil---where DARC polymorphism remains prevalent and emph{P. vivax} cases persist---we calibrate the model and explore how changes in DARC genotype frequencies impact malaria burden. Our analysis determines the threshold proportion of Duffy-negative individuals required to achieve population-wide protection against emph{P. vivax}, and quantifies how varying levels of Duffy negativity affect monthly incidence patterns.

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Annual Meeting for the Society for Mathematical Biology, 2025.