Stability analysis of a reaction–diffusion HIV immune model with absorption effect

In this article, a reaction–diffusion model of HIV immunity with chemotaxis and absorption effect is constructed. The paper proves the existence and boundedness of the global classical solution of this mode when the chemotactic coefficient is kept in a suitable range. Five equilibrium points are established based on the different ranges of the basic regeneration number, two immune reproduction numbers and the immune competitive reproduction number. The global asymptotic stability of each equilibrium point is established by constructing an appropriate Lyapunov function when the chemotactic coefficient is kept in a small interval.