Age-structured within-host HIV dynamics with multiple target cells

Abstract

Human immunodeficiency virus (HIV) can infect various types of cell populations such as CD4+ T cells and macrophages. The heterogeneity of these target cells implies different birth, death, infection rates, and so on. To investigate the within-host dynamics of HIV which can infect n different types of target cells, a theoretical model with infection-age structure for each type of target cells and a general nonlinear incidence rate is proposed in this manuscript. The model, in the form of a hyperbolic system of partial differential equations (PDE) for infected target cells coupled with several ordinary differential equations, is shown to be biologically reasonable with the establishment of existence, positivity, and boundedness of solutions. Although the PDE form poses novel challenges to theoretical investigation, rigorous analysis is performed to show the uniform persistence of the virus when the basic reproduction number is greater than one. Furthermore, by constructing suitable Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than unity, while the positive steady state is globally asymptotically stable when the basic reproduction number is greater than one.