A Multi-Strain Virus Model with Infected Cell Age Structure: Application to HIV

Abstract

We consider a general mathematical model of a within-host viral infection with $n$ virus strains and explicit age-since-infection structure for infected cells. In the model, multiple virus strains compete for a population of target cells. Cells infected with virus strain $i\in \left\{1,...,n\right\}$ 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, ${\mathcal{R}}_i$, and a corresponding positive single strain equilibrium, $E_i$, when ${\mathcal{R}}_i>1$. If ${\mathcal{R}}_i<1$, then the total concentration of virus strain $i$ will converge to 0 asymptotically. The main result is that when ${\max }_i{\mathcal{R}}_i>1$ and all of the reproduction numbers are distinct, i.e. ${\mathcal{R}}_i\ne {\mathcal{R}}_j\forall i\ne j$, 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.

arXiv commentMinor revisions performed; reworked Figure 2