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We consider a general mathematical model of a within-host viral infectionwith $n$ virus strains and explicit age-since-infection structure for infectedcells. In the model, multiple virus strains compete for a population of targetcells. Cells infected with virus strain $i\in\left\{1,...,n\right\}$ die atper-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 ofthe 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 virusstrain $i$ 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.$\mathcal{R}_i\neq \mathcal{R}_j \ \forall i\neq j$, the viral strain with themaximal basic reproduction number competitively excludes the other strains. Asan application of the model, HIV evolution is considered and simulations areprovided.

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