A multi-strain virus model with infected cell age structure: Application to HIV

A general mathematical model of a within-host viral infection with n virus strains and explicit age-since-infection structure for infected cells is considered. In the model, multiple virus strains compete for a population of target cells. Cells infected with virus strain i is an element of {1, ..., n} die at per-capita rate delta(i)(a) and produce virions at per-capita rate p(i)(a), where delta(i)(a) and p(i)(a) are functions of the age-since-infection of the cell. Viral strain i has a basic reproduction number, R-i, and a corresponding positive single strain equilibrium, E-i, when R-i > 1. If R-i < 1, then the total concentration of virus strain i will converge to 0 asymptotically. The main result is that when max(i) R-i > 1 and all of the reproduction numbers are distinct, i.e. R-i not equal R-j for all(i) not equal j, the viral strain with the maximal basic reproduction number competitively excludes the other strains. As an application of the model, HIV evolution is considered and simulations are provided. (C) 2014 Elsevier Ltd. All rights reserved.