Dynamics of a delayed integro-differential HIV infection model with multiple target cells and nonlocal dispersal

Abstract

In this paper, we formulate an age-space-structured HIV infection model that incorporating infection age, multiple target cells, and nonlocal dispersal. Applying the characteristic line method, we reduce the infection-age model to a delayed integro-differential system. The global well-posedness and boundedness of the semiflow for the system are established. The principal eigenvalue of the nonlocal dispersal problem is formulated, and it plays the same role as the basic reproduction number $$R_0$$ (the spectral radius of the next generation operator), which determines the global behavior of the steady states of the system. More precisely, the infection-free steady state is globally asymptotically stable (g.a.s) when $$R_0<1$$ , the virus is always present and the infected steady state is g.a.s when $$R_0>1$$ . Numerical simulations are carried out reinforcing these analytical results. In particular, three different kernel functions are given out to study the impact of dispersal form on the HIV infection within the host. Finally, our simulation works show that (i) increasing the dispersal rate and decreasing the intracellular delay will be increasing the final viral loads; (ii) the dispersal kernel function affects the value of $$R_0$$ and the final viral loads, and it is revealed that the dispersal form plays a crucial role in the process of HIV infection within the host.