Mathematical Biology Seminar

Date: October 18, 2021

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Jay Walton, Texas A&M University

Title: A Hybrid Nonlinear Reaction-Diffusion, First-Order-Hyperbolic System Arising from a New Approach to Structured Population Dynamics

Abstract: This talk considers population dynamics taking account of: (i) population structure such as age, stage, size and biomass; (ii) structure modulated population spatial mobility; (iii) structure modulated population growth including both hyperplasia (population number change) and hypertrophy (individual biomass change). Population structural features are modeled via space/time field variables rather than the traditional approach of introducing structure parameters as additional independent variables. In the special case of diffusive transport and mass or size structure, conservation postulates for these new structure field variables along with standard conservation postulates for population number lead to a hybrid nonlinear reaction-diffusion, first-order-hyperbolic system of PDEs. Results on various qualitative properties of this novel system are presented along with application to an aquatic species subject to harvesting. In particular, the model is used to study optimal configurations for marine protective areas designed to prevent catastrophic population collapse from over harvesting.