A Network Immuno-Epidemiological HIV Model.

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number R 0 of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when R 0 < 1 and unstable when R 0 > 1 . Numerical simulations suggest that R 0 increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes. [ABSTRACT FROM AUTHOR]