Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

In this article, we investigate a diffusive two-strain epidemic model with non-monotone incidence rate and virus mutation. The positivity, existence and uniform boundedness of the solutions of the model system are studied. It is found that the system has three equilibrium points, namely the infection-free equilibrium point, the strain-2 endemic equilibrium point and both the strain-1 and strain-2 endemic equilibrium points. The global asymptotic stability analysis of the diffusive model system near all the equilibrium points is carried out by constructing appropriate Lyapunov functional. It is found that the system has no strain-1 endemic equilibrium point possibly due to the virus mutation. So, in this type of diseases, the infection due to strain-1 cannot be persistent in the community.

Dynamics of a stochastic periodic SIRS model with time delay

Dynamical behaviors of a stochastic periodic SIRS epidemic model with time delay are investigated. By constructing suitable Lyapunov functions and applying Itô’s formula, the existence of the global positive solution and the property of stochastically ultimate boundedness of model (1.1) are proved. Moreover, the extinction and the persistence of the disease are established. The results are verified by numerical simulations.