A multi-strain virus model with infected cell age structure: Application to HIV. (April 2015) - Browne, Cameron J.
Abstract: 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 ∈ { 1, …, n } die at per-capita rate δ i ( a ) and produce virions at per-capita rate p i ( a ), where δ 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 ≠ R j ∀ 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.