2018-06-29 10:00-11:00 Room 1418, Sciences Building No. 1

Abstract: We formulate a general impulsive reaction-diffusion-advection equation model to describe the population dynamics of species with distinct reproductive and dispersal stages. The seasonal reproduction is modeled by a discrete-time map, while the dispersal is modeled by a reaction-diffusion-advection partial differential equation. Study of this model requires a simultaneous analysis of the differential equation and the recurrence relation. When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of the species arises, depending on the size and geometry of the domain. We show that there exists an extreme volume size such that if the region size falls below this size the species is driven extinct, regardless of the geometry of the domain. To construct such extreme volume sizes and critical domain sizes, we apply the classical Rayleigh-Faber-Krahn inequality and the spectrum of uniformly elliptic operators. The critical domain results provide qualitative insight regarding long-term dynamics for the model. Last, we provide applications of our main results to certain biological reaction-diffusion models regarding marine reserve, terrestrial reserve, insect pest outbreak, and population subject to climate change.

This is a joint work with Mostafa Fazly (University of Texas at San Antonio) and Mark A. Lewis (University of Alberta).

Bio: Dr. Hao Wang is currently a tenured faculty member at the University of Alberta. His research has been funded by NSERC, MITACS, OSRIN, PIMS, and the Province of Alberta. He has supervised more than 20 trainees at all levels, including 3 PDFs. He received the Early Career Award from MBI (United States) in 2013. He is an editor/associate editor/regional editor for several journals in United States and Europe.

Dr. Wang’s research program is truly interdisciplinary at the interface of mathematical, computational, and experimental studies. His research focuses on differential equations and their applications in life sciences. Via multiscale modeling (multiple scales of time and/or space), he has fulfilled many significant research accomplishments in the areas of stoichiometric modeling, microbiology, ecotoxicology, species invasions, and infectious diseases. His research group actively collaborates with biologists, engineers, industrial partners and governments, to explore and resolve urgent environmental problems. Many of his mathematical models are tested and calibrated by laboratory and/or field experiments. At the University of Alberta, Dr. Wang is leading several interdisciplinary modeling projects on estimation and reduction of greenhouse gas emissions from biodegradation in oil sands industry, impacts of industrial toxins on ecosystems using the stoichiometric approach, control of invasive species in North America, spatial modeling of animal movements, and transmission of infectious disease using an inverse method and fully controlled fish-based lab experiments.