Spreading and vanishing in a West Nile virus model with expanding fronts

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（5）
• 页码范围: 841-860
• 页数: 20页
• 语种: 英文
• DOI: 10.1007/s11425-016-0367-4

摘要

We study a simplified version of a West Nile virus (WNv) model discussed by Lewis et al.(2006),which was considered as a first approximation for the spatial spread of WNv.The basic reproduction number R0 for the non-spatial epidemic model is defined and a threshold parameter RoD for the corresponding problem with null Dirichlet boundary condition is introduced.We consider a free boundary problem with a coupled system,which describes the diffusion of birds by a PDE and the movement of mosquitoes by an ODE.The risk index R0F (t) associated with the disease in spatial setting is represented.Sufficient conditions for the WNv to eradicate or to spread are given.The asymptotic behavior of the solution to the system when the spreading occurs is considered.It is shown that the initial number of infected populations,the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus.Numerical simulations are presented to illustrate the analytical results.