In this paper,we study some models with repulsion effect on superinfecting viruses by infected cells{■T/■t=DT△T(x,t)-■(TФ(T,I)■I)+h(x)-dTT(x,t)-β(x)T(x,t)V(x,t),■I/■T=DT△I+β(x)T(x,t)V(x,t)-dII(xt,),■I/■T=...In this paper,we study some models with repulsion effect on superinfecting viruses by infected cells{■T/■t=DT△T(x,t)-■(TФ(T,I)■I)+h(x)-dTT(x,t)-β(x)T(x,t)V(x,t),■I/■T=DT△I+β(x)T(x,t)V(x,t)-dII(xt,),■I/■T=■(Dv(I)■V)+γ(x)I(x,t)-dvV(x,t),where T(x,t),I(x,t)and V(x,t)are the density of uninfected cells,infected cells and viruses at time t at location x,respectively.The functions h(x),β(x)andγ(x)are assumed to be positive,continuous and bounded.h(x)denotes the production rate of uninfected cells.The infection rate isβ(x)and the functionγ(x)is the production rate of free viruses.Andβ(x)T(x,t)V(x,t)is the rate of transfer from uninfected cells to infected cells.The positive constants dT,dI and dV denote the death rate of uninfected cells,infected cells and viruses,respectively.The stability of the infection-free equilibrium solution and infection equilibrium solution is discussed.It is shown that if the basic reproduction number R0≤1 then the chemotaxis has no effect,that is,the infection-free constant solution is stable.For the system with chemotactic sensitivityФ(T,I)=1-T,if R0>1,then the infection constant solution will be unstable under some conditions.展开更多
基金This work was supported by the National Natural Science Foundation of China(11871238).
文摘In this paper,we study some models with repulsion effect on superinfecting viruses by infected cells{■T/■t=DT△T(x,t)-■(TФ(T,I)■I)+h(x)-dTT(x,t)-β(x)T(x,t)V(x,t),■I/■T=DT△I+β(x)T(x,t)V(x,t)-dII(xt,),■I/■T=■(Dv(I)■V)+γ(x)I(x,t)-dvV(x,t),where T(x,t),I(x,t)and V(x,t)are the density of uninfected cells,infected cells and viruses at time t at location x,respectively.The functions h(x),β(x)andγ(x)are assumed to be positive,continuous and bounded.h(x)denotes the production rate of uninfected cells.The infection rate isβ(x)and the functionγ(x)is the production rate of free viruses.Andβ(x)T(x,t)V(x,t)is the rate of transfer from uninfected cells to infected cells.The positive constants dT,dI and dV denote the death rate of uninfected cells,infected cells and viruses,respectively.The stability of the infection-free equilibrium solution and infection equilibrium solution is discussed.It is shown that if the basic reproduction number R0≤1 then the chemotaxis has no effect,that is,the infection-free constant solution is stable.For the system with chemotactic sensitivityФ(T,I)=1-T,if R0>1,then the infection constant solution will be unstable under some conditions.
