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New insights into COVID-19 modeling

The COVID-19 pandemic has led to an unprecedented worldwide response to grapple with the fast spreading virus.

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Our applied mathematics group was well represented at the 4th Annual Meeting of the SIAM Texas-Louisiana Section on November 5-7, 2021 at South Padre Island, Texas. Bruce Wade and Joshua Caleb Macdonald organized minisymposia (special sessions). Bruce Wade, Joshua Caleb Macdonald, Cameron Browne, Hayriye Gulbudak, and Amy Veprauskas presented talks. Details are given below.

Minisymposium 6. Complex Adaptive Systems in Life and Social Sciences

Organizers: Lucero Rodriguez Rodriguez, Arizona State University; Yun Kang, Arizona State University; Jordy Cevallos-Chavez, Arizona State University

Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China

Hayriye Gulbudak
University of Louisiana at Lafayette
Abstract: By mathematical modeling lockdowns and contact tracing as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed.

Modeling COVID-19 outbreaks in United States with distinct testing, lockdown speed and fatigue rates

Cameron Browne
University of Louisiana at Lafayette
Abstract: Each state in the United States exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing. In this study, via per-capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown/selfquarantine entry and exit rates (representing government and behavioral reaction), along with the true number of cases in first phase of epidemic. We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, and critical population quarantine ”half-life” of 30 days independent of other model parameters.

Examining the effect of frequency-dependent and independent selection on the dynamics of a predator-prey system

Amy Veprauskas
University of Louisiana at Lafayette
Abstract: We apply a Darwinian dynamics framework to study ecological and evolutionary processes occurring on commensurate timescales. Two types of selection are compared: frequency-independent selection in which an individual’s fitness depends solely on its own trait, and frequency-dependent selection where their fitness also depends on the traits of others. Our main application is a discrete-time predator-prey system where the prey evolves due to an environmental stressor. Under frequency-independent selection, slow evolution describes a continuous perturbation of the non-evolutionary system, while fast evolution destabilizes dynamics via a period-doubling bifurcation. Meanwhile, frequency-dependent selection may destabilize dynamics, even for slow evolution, via a Neimark-Sacker bifurcation.


Minisymposium 17. Operator Splitting Methods and Adaptive Schemes for Systems of Nonlinear Evolution Equations

Organizer: Bruce Wade, University of Louisiana at Lafayette

Dimensional Splitting with Exponential Time Differencing Schemes for Advection-Diffusion-Reaction Systems

Bruce Wade
University of Louisiana at Lafayette
Abstract: Dimensional splitting formulation for Exponential Time Differencing (ETD) schemes is advantageous for advection-diffusion-reaction systems. These methods are introduced and analyzed for their effectiveness, including smoothing properties when applied to systems with nonsmooth or mismatched data. Several dimensional splitting strategies are presented, with an analysis of speedup. Robust performance under a variety of types of problems is empirically developed.


Minisymposium 22. Reproducibility, Reliability, and Robustness: Confronting Models from Across Mathematical Biology with Data

Organizers: Joshua Caleb Macdonald, University of Louisiana at Lafayette; Juan B. Gutierrez, University of Texas at San Antonio

Infectious disease dynamics necessarily operate across biological scales

Joshua Caleb Macdonald
University of Louisiana at Lafayette
Abstract: We investigated within-host dynamics and among-host transmission of three strains of highly contagious, directly transmitted foot-and-mouth disease viruses (FMDVs) in their wildlife reservoir host, African buffalo. We combined data on viral dynamics, immune responses of buffalo experimentally infected with southern African territories serotypes of FMDV (SAT1, 2, 3) with non-linear ODE models to ask (i) How does the route of infection affect within-host dynamics? (ii) How do viral and immune dynamics vary among FMDV strains?; and (iii) Which viral and immune parameters determine viral replication within and transmission among hosts?

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