Analysis of a within-host age-structured model with mutations between two viral strains

In this paper, we study a within-host age-structured model with mutation and back mutation, which is in the form of partial differential equations with double-infections by two strains of viruses. For the case that the production rates of viruses are gamma distributions, the PDE model is transformed into an ODE one. To explore the effect of mutations, we analyze our model without mutations first. In this case, two strains of viruses are proved to die out when both of the individual reproductive numbers are less than one; otherwise, their evolution will comply with competitive exclusion principle meaning that the stronger one will survive finally. Then, the mutations are considered in the model. We verify that there may exist a coexistence equilibrium which is globally asymptotically stable under some specific conditions about mutation rates. Therefore, mutations can lead to coexistence of two strains.