A reaction-diffusion within-host HIV model with cell-to-cell transmission

摘要

In this paper, a reaction-diffusion within-host HIV model is proposed. It incorporates cell mobility, spatial heterogeneity and cell-to-cell transmission, which depends on the diffusion ability of the infected cells. In the case of a bounded domain, the basic reproduction number R-0 is established and shown as a threshold: the virus-free steady state is globally asymptotically stable if R-0 1 and the virus is uniformly persistent if R-0 1. The explicit formula for R-0 and the global asymptotic stability of the constant positive steady state are obtained for the case of homogeneous space. In the case of an unbounded domain and R-0 1, the existence of the traveling wave solutions is proved and the minimum wave speed c* is obtained, providing the mobility of infected cells does not exceed that of the virus. These results are obtained by using Schauder fixed point theorem, limiting argument, LaSalle's invariance principle and one-side Laplace transform. It is found that the asymptotic spreading speed may be larger than the minimum wave speed via numerical simulations. However, our simulations show that it is possible either to underestimate or overestimate the spread risk R-0 if the spatial averaged system is used rather than one that is spatially explicit. The spread risk may also be overestimated if we ignore the mobility of the cells. It turns out that the minimum wave speed could be either underestimated or overestimated as long as the mobility of infected cells is ignored.