The theory of the principal eigenvalue is developed for an elliptic eigenvalue problem associated with a linear parabolic cooperative system with some zero diffusion coefficients. Then the basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure. These theoretical results are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.

Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models

A spatial SIS model in advective heterogeneous environments

Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments

A SIS reaction–diffusion–advection model in a low-risk and high-risk domain ☆

Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism

In this paper, we consider a susceptible–infected–susceptible (SIS) reaction–diffusion model, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and temporally periodic and the total population number is constant. We introduce a basic reproduction number and establish threshold-type results on the global dynamics in terms of . In particular, we obtain the asymptotic properties of with respect to the diffusion rate dI of the infected individuals, which exhibit the delicate influence of the time-periodic heterogeneous environment on the extinction and persistence of the infectious disease. Our analytical results suggest that the combination of spatial heterogeneity and temporal periodicity tends to enhance the persistence of the disease.

https://iopscience.iop.org/article/10.1088/0951-7715/25/5/1451/pdf

Rui Peng

Papers

A reaction-diffusion SIS epidemic model in a time-periodic environment