Stability and Persistence of an Age Structured Epidemic Model with Mutation and Vaccination

Abstract

In this paper, we propose an age-structured epidemic model with strain mutation and age-based vaccination. We define the reproduction numbers of both the original and mutant strains ($R_{0}^{1}$ and $R_{0}^{2}$). If the reproduction number $R_{0} < 1$, the disease-free steady state is locally asymptotically stable. If the reproduction number $R_{0}^{2} > 1$, there exists a dominant steady state of the mutant strain. Conditions for local stability of this dominant steady state are also obtained. If both reproduction numbers $R_{0}^{1}$ and $R_{0}^{2}$ are greater than 1, a coexistence steady state may occur. Finally, the uniform persistence of the disease described by our age-structured model is strictly proved when the reproduction number $R_{0}^{1} > 1.$ By using the data of the COVID-19 epidemic in Wuhan and the theoretical results obtained in this paper, some numerical calculations are carried out to demonstrate the effect of the age-based vaccination strategy.