Global dynamics of a reaction and diffusion model for an HTLV-I infection with mitotic division of actively infected cells

This paper is concerned with the global dynamics of a reaction and diffusion model for an HTLV-I infection with mitotic division of actively infected cells and CTL immune response. The well posedness of the proposed model is investigated. In the case of a bounded spatial domain, we establish the threshold dynamics in terms of the basic reproduction number $mathcal{R}_0$ for the spatially heterogeneous model. Also, by means of different Lyapunov functions, the global asymptotic properties of the steady states for the spatially homogeneous model are studied. In the case of an unbounded spatial domain, there are no travelling wave solutions connecting the infection-free steady state with itself when $mathcal{R}_0 < 1$. Finally, numerical simulations and conclusions are given.