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 R_0 for the non-...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 R_0 for the non-spatial epidemic model is defined and a threshold parameter R_0~D 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 R_0~F(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.展开更多
In this paper,we investigate a reaction-diffusion-advection model with expanding fronts,which models the spatial transmission of West Nile virus(WNv)in a heterogeneous environment.A free boundary problem is formulated...In this paper,we investigate a reaction-diffusion-advection model with expanding fronts,which models the spatial transmission of West Nile virus(WNv)in a heterogeneous environment.A free boundary problem is formulated and the global existence and uniqueness of the solution is presented.In addition to a classical basic reproduction number,the spatial-temporal basic reproduction number for the model with null Dirichlet boundary condition is introduced and the risk index associated with the virus in spatial setting is defined,and their properties are discussed.Sufficient conditions for the WNv to vanish or spread are given,and the asymptotic behavior of the solution to the free boundary problem when the spreading occurs is established.Our results show that the initial number of infected populations and the expanding capability of the expanding fronts exhibit important impacts on the extinction or persistence of the virus.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11371311)Top-Notch Academic Programs Project of Jiangsu Higher Education Institutions(Grant No.PPZY2015B109)
文摘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 R_0 for the non-spatial epidemic model is defined and a threshold parameter R_0~D 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 R_0~F(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.
基金supported by the Natural Science Foundation of China(11872189,11472116).
文摘In this paper,we investigate a reaction-diffusion-advection model with expanding fronts,which models the spatial transmission of West Nile virus(WNv)in a heterogeneous environment.A free boundary problem is formulated and the global existence and uniqueness of the solution is presented.In addition to a classical basic reproduction number,the spatial-temporal basic reproduction number for the model with null Dirichlet boundary condition is introduced and the risk index associated with the virus in spatial setting is defined,and their properties are discussed.Sufficient conditions for the WNv to vanish or spread are given,and the asymptotic behavior of the solution to the free boundary problem when the spreading occurs is established.Our results show that the initial number of infected populations and the expanding capability of the expanding fronts exhibit important impacts on the extinction or persistence of the virus.