A delayed reaction–diffusion viral infection model with nonlinear incidences and cell-to-cell transmission  

作　　者：Qing Ge Xia Wang Libin Rong 

机构地区：[1]School of Mathematics and Statistics,Xinyang,Normal University,Xinyang 464000,P.R.China [2]Department of Mathematics,University of Florida,Gainesville,FL 32611,USA

出　　处：《International Journal of Biomathematics》2021年第8期305-342,共38页生物数学学报（英文版）

基　　金：Wang is supported by the NSFC(Nos.11771374,12026204 and 12171413);the Program for Science and Technology Innovation Teams in Henan(21IRTSTHN014);Rong is supported by the NSF grants DMS-1758290 and DMS-1950254.

摘　　要：In this paper,we propose a reaction–diffusion viral infection model with nonlinear incidences,cell-to-cell transmission,and a time delay.We impose the homogeneous Neumann boundary condition.For the case where the domain is bounded,we first study the well-posedness.Then we analyze the local stability of homogeneous steady states.We establish a threshold dynamics which is completely characterized by the basic reproduction number.For the case where the domain is the whole Euclidean space,we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder’s fixed point theorem.Finally,we study how the speed of spread in space affects the spread of cells and viruses.We obtain the existence of the wave speed,which is dependent on the diffusion coefficient.

关 键 词：Reaction-diffusion equation cell-to-cell transmission absorption effect time delay traveling wave solutions 

分 类 号：O17[理学—数学]