Math Bio Seminar 2025 Fall Schedule

We meet on Wednesdays from 3:00 to 3:50 PM (EST) in Ayres 122.

Sept 10

Speaker: Xiang-Sheng Wang (University of Louisiana at Lafayette)

Title: Numerical Optimal Control of Metastatic Cancer Treatment Models

Abstract: We propose a unified size-structured PDE model for metastatic tumor growth, extending a well-known coupled ODE–PDE framework from the literature. Using optimal control theory, we investigate a treatment model based on this formulation, derive the first-order necessary optimality system, and show that the uniqueness of the optimal control depends on the chosen objective functional. To improve computational efficiency, we reformulate the transport PDE model as a lumped ODE system that incorporates a Volterra integral equation of convolution type, independent of the control variable. This reduction allows computation of aggregated tumor dynamics without explicit spatial dependence. Nonlinear pharmacokinetic and pharmacodynamic effects of treatment are also incorporated into the lumped model. Numerical experiments demonstrate biologically relevant treatment outcomes across different models and control strategies.

Sept 17

Speaker: Fanze Kong (University of Washington)

Title: Global well-posedness and concentrated steady states in chemotaxis-fluid models

Abstract: Chemotaxis is a process by which bacteria direct their movement in response to chemical stimulus gradients. To describe this phenomenon, E. Keller and L. Segel in the 1970s proposed a class of strongly coupled parabolic PDEs, now known as Keller-Segel (KS) models. Due to their relatively simple structures yet rich dynamical behaviors, KS systems have attracted extensive attention, with numerous studies devoted to the qualitative properties of the solutions, including global well-posedness, singularity formation, etc. In this talk, we focus on a class of Keller–Segel–Navier–Stokes (KS-NS) systems, which serve as a paradigm for modeling the chemotactic movement of bacteria in a viscous fluid. Under the assumption of small cellular initial mass, we establish the existence of global-in-time solutions to the two-dimensional KS–NS system by employing the entropy–dissipation method. Moreover, we construct spot steady states at the critical mass threshold for the cellular density using the inner–outer gluing approach.

Sept 24

Speaker: John McAlister (University of Tennessee, Knoxville)

Title: Replicator Dynamics with Spatial Structure for Evolutionary Games

Abstract: The replicator equation has been widely used as a fundamental model in evolutionary game theory. However, the model requires the assumption that populations are arbitrarily large and well mixed, so using the replicator equation to describe dynamics of games with explicit relational structure has been impossible. Here I present a reshaping of the replicator equation model for use in high structure multiplayer games through the use of mixed strategies and show that the resulting system satisfies the folk theorem of Evolutionary Game Theory: (a) Every stable equilibrium is a Nash equilibrium, (b) convergent trajectories converge to Nash equilibria, and (c) Strict Nash equilibria are locally asymptotically stable. Having shown this, I examine the coordination game in particular and classify, in part, the system dynamics in neighborhoods of different types of Nash equilibria and discuss how these continuous dynamics give us insights into the classical game.

Oct 8

Speaker: Leili Shahriyari (University of Massachusetts, Amherst)

Title: Data Driven QSP Modeling of Cancer: A Step Toward Personalized Treatment

Abstract: Our goal is to create personalized computational models of cancer to better understand how an individual’s disease progresses. By simulating the unique characteristics of each tumor and its response to treatment, we aim to provide insights that support personalized cancer care. To achieve this, we combine mechanistic modeling with machine learning techniques to generate individualized predictions. A central element of our approach is a mechanistic model based on quantitative systems pharmacology (QSP), a computational method used to analyze drug interactions and effects. Our QSP model incorporates a large system of nonlinear equations that represent both biochemical and biomechanical processes within tumors. One common challenge in QSP is parameter estimation, as traditional models often assume uniformity across patients. This assumption can limit accuracy when calibrating models with diverse patient data. To address this, we present a computational framework that focuses on individual patient data for parameter estimation, tailoring QSP model parameters to reflect each person’s unique tumor biology. We conduct sensitivity analyses and uncertainty quantification to identify critical interactions and define prediction ranges. By integrating this patient-specific QSP framework with insights into cellular and molecular interactions, we aim to better predict cancer progression and treatment response. While we recognize the challenges and complexities of this work, we are optimistic about its potential to advance personalized cancer therapy.

Oct 15

Speaker: Amber Young (University of Tennessee, Knoxville)

Title: Modeling La Crosse Virus in North Carolina and Tennessee: Mosquito Activity and Human Infection

Abstract: La Crosse Virus (LACV) is a mosquito-borne disease that is spread via the bite of an infected \textit{Aedes} mosquito, with most reported cases occurring in individuals under 20 years old. Individuals with LACV may also develop La Crosse Encephalitis, but most cases are asymptomatic and go unreported. In recent years, counties in North Carolina and Tennessee have been identified as hotspots for the virus. Humans serve as dead-end hosts and therefore do not play a role in LACV transmission. Using a system of ordinary differential equations, we developed the first model that accounts for inter- and intra-year variability of LACV transmission in mosquito and human populations in western North Carolina and eastern Tennessee. Environmental effects on mosquito populations were incorporated through non-decreasing, time-varying functional forms of precipitation and temperature. Human demographics were parameterized using population data, while yearly case data and past seroprevalence studies were used to estimate human transmission rates.

Oct 29

Speaker: Elisha Brooks (University of Tennessee, Knoxville)

Title: Quantifying Mortality Risk: A decision-theoretic framework for county-level risk in opioid mortality

Abstract: Understanding and mitigating county-level disparities in opioid overdose mortality requires both accurate prediction of mortality rates and a reliable identification of where those predictions fail. In this study, we present a decision-theoretic framework for empirical risk quantification that measures the stability and predictability of opioid mortality across US counties from 2010-2022.

We utilize this risk quantification to identify counties that are structurally volatile: places where social, economic, or infrastructural factors cause mortality dynamics to diverge from model expectations. We integrate this with the CDC Social Vulnerability Index and USDA urbanicity classification to characterize the socioeconomic profiles of high risk counties. This provides a principled way to identify underlying factors that might be contributing to these volatilities, offering policy-makers a data-driven foundation for more informed intervention strategies.

Nov 5

Speaker: Kennedi Hambrick (University of Tennessee, Knoxville)

Title: TBD

Abstract: TBD

Nov 12

Speaker: Madison Pratt (University of Tennessee, Knoxville)

Title: TBD

Abstract: TBD

Nov 19

Speaker: Andy Bernoff (Harvey Mudd College)

Title: Agent-Based and Continuous Models of Locust Hopper Bands

Abstract: An outstanding challenge in mathematical biology is using laboratory and/or field observations to tune a model’s functional form and parameter values. These problems lie at the intersection of dynamical systems and data science. In this talk I will discuss an ongoing project developing models of the Australian plague locust for which excellent field data is available. Under favorable environmental conditions flightless juveniles aggregate into coherent, aligned swarms referred to as hopper bands. We develop two models of hopper bands in tandem; an agent-based model that tracks the position of individuals and a continuum model describing locust density. By examining 4.4 million parameter combinations, we identify a set of parameters that reproduce field observations.

I will then discuss ongoing efforts to improve these models. The first extends this work by modeling locust alignment via the Kuramoto model of oscillator synchronization. The second uses motion tracking of tens of thousands of locusts to shed light on how locust movement is influenced by social interactions. Finally, we reflect on how recent lab work is revolutionizing our understanding of locust visual perception and navigation, spawning a new class of agent-based models.