Global Dynamics on a Reaction-Diffusion HIV Coinfection Model Between CD4+ T Cell and Macrophages with Humoral Immunity (pp.79-106)

In this paper, a reaction-diffusion HIV coinfection model between CD4 + T cells and macrophages with humoral immunity and recovery of infected CD4 + T cell is proposed in heterogeneous environment.First, the existence and ultimate boundedness of global solutions are discussed, the basic reproduction number ℜ0 is obtained.Second, criteria on the globally asymptotic stability of infection-free steady state is established if ℜ0 < 1, the uniform persistence of disease is obtained if ℜ0 > 1 in the absence of humoral immune response.Furthermore, the immune response reproduction number R1 is calculated under the homogeneous environment, by which criteria on the globally asymptotic stability of humoral immune-free equilibrium and chronic-infection equilibrium are obtained, respectively.Finally, the theoretical results are demonstrated by numerical simulations, we find that ignoring the HIV infection with macrophages will underestimate the viral loads of HIV within body, meanwhile, diffusion could cause great impact on HIV spread, it could change the situation of HIV infection at some positions from no infection to infection.