Analysis Of Virus Dynamics Model With Age Of Infection And Immunizing Response

The mathematical modeling and study of infection of virus within-host is a important topic in immunological dynamics. In this paper, one strain viral model and multi-strain viral model with age of infection and immunity response are formulated and analyzed. The explicit expression of basic reproduction numbers corresponding to the two models are given. By constructing suitable Lyapunov functions, it is shown that the infection free equilibriums are globally asymptotical stable if the basic reproduction numbers are less than1, in this case, the virus will die out within-host. If the basic reproduction numbers are greater than1, the infection free equilibriums are unstable, and if the infection equilibriums exists, the infection equilibriums are globally asymptotical stable, in this case, the virus will persist within-host.