Multi-strain virus dynamics with mutations: A global analysis

We consider within-host virus models with more than one strain and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Moreover, using a perturbation result due to Smith and Waltman, we show that this steady state also preserves global stability.

💡 Research Summary

The paper develops a within‑host viral dynamics framework that simultaneously accounts for multiple competing strains and the possibility of mutation among them. Starting from the classical single‑strain model, the authors introduce N strains, each characterized by its own replication rate, death rate, and immune‑evasion parameters. Mutations are represented by a directed graph G whose vertices correspond to strains and whose edges (i→j) indicate that strain i can mutate into strain j with a small rate μ_{ij}. The resulting system of ordinary differential equations reads

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