title: Travelling waves of a delayed SIR epidemic model with nonlinear incidence rate and spatial diffusion.
abstract: This paper is concerned with the existence of travelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.
authors: Department of Physiology, Hebei Medical University, Shijiazhuang, People's Republic of China.
authors: Jing
authors: J
authors: Yang
authors: Siyang
authors: S
authors: Liang
authors: Yi
authors: Y
authors: Zhang
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D004058:Diffusion; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D014195:Travel