An epidemic model with viral mutations and vaccine interventions

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration. We discuss and analyze the existence and stability of equilibrium points. This model has three types of equilibrium points, namely disease-free equilibrium, dominance equilibrium point of strain two, and coexistence endemic equilibrium point. The local stability of the dominance equilibrium point of strain two and coexistence endemic equilibrium point are verified by using the Routh--Hurwitz criteria, while for the global stability of the dominance equilibrium point of strain two, we used a suitable Lyapunov function. We also carried out the bifurcation analysis using the application of center manifold theory, and we obtained that the system near the disease-free equilibrium point always has supercritical bifurcation. Finally, the numerical simulations are provided to validate the theoretical results. Continuation of the supercritical bifurcation point results in two Hopf bifurcations indicating a local birth of chaos and quasi-periodicity.