UAlberta Math Biology Seminar: Guodong Liu

The nonlinear incidence mechanism is a more general disease transmission mechanism to fit the data in clinical observations or laboratory experiments. In a heterogeneous environment, how to describe the cognitive dispersal of individuals is also an essential issue in epidemic modelling. In this talk, I will introduce two reaction-diffusion susceptible-infected-susceptible epidemic models with nonlinear incidence and cognitive diffusion, using Fick’s diffusion law and Fokker-Planck diffusion law, respectively. Then I will present a bootstrap argument to derive the boundedness of solutions due to the difficulties caused by the nonlinear incidence. Comparing the cognitive diffusion models with a homogeneous diffusion model and an ordinary differential equation model, we explore the effects of diffusion patterns, dispersal rates, values of exponentials, and favourableness of habitats on spatial segregation between susceptible and infected individuals.

This is joint work with my supervisors, H. Wang and X. Zhang.