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

A general mathematical model of a within-host viral infection with nn 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∈{1,…,n}i∈{1,…,n} die at per-capita rate δi(a)δi(a) and produce virions at per-capita rate pi(a)pi(a), where δi(a)δi(a) and pi(a)pi(a) are functions of the age-since-infection of the cell. Viral strain ii has a basic reproduction number, RiRi, and a corresponding positive single strain equilibrium, EiEi, when Ri>1Ri>1. If Ri<1Ri<1, then the total concentration of virus strain ii will converge to 00 asymptotically. The main result is that when maxiRi>1maxiRi>1 and all of the reproduction numbers are distinct, i.e. Ri≠Rj∀i≠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.