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

摘要

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 iΕ{1,&mellip;,n} die at per-capita rate δi(a) and produce virions at per-capita rate pi(a), where δi(a) and pi(a) are functions of the age-since-infection of the cell. Viral strain i has a basic reproduction number, Ri, and a corresponding positive single strain equilibrium, Ei, when Ri>1. If Ri<1, then the total concentration of virus strain i will converge to 0 asymptotically. The main result is that when maxiRi>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.

关键词