A Spatiotemporal Model For HIV And Immune Response Dynamics

This paper deals with a spatiotemporal model for interactions between virus,susceptible cells and immune cells.AS long as virus infect susceptible cells,immune cells kill the virus by mean of immune dynamics;along with the virus being killed,the number of infected cells decreases;and then the number of immune cells decreases. The above process repeats continually.So the interactions between virus,susceptible cells and immune cells are complicated.The model consists of three reaction-diffusion partial differential equations.The model is analyzed by the theory of partial differential equations.The local existence and uniqueness of solutions is first proved by the fixed point theorem.Then, based on Schauder theory and L~p theory of parabolic equations,the global existence and uniqueness of classical solutions to this model is showed.Furthermore,the nonlinear stability of three constant solutions is studied,and the nonexistence of non-constant steady states is also discussed.