Extinction, persistence and density function analysis of a stochastic two-strain disease model with drug resistance mutation

Drug resistance is a global health and development threat. However, its effect of emergence on disease dynamics is still poorly understood. In this paper, we develop a novel stochastic epidemic model where drug-sensitive and drug-resistant infected groups interact through the mutation. Firstly, we propose and prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the extinction and persistence of the drug-sensitive and drug-resistant infections are investigated. By constructing appropriate Lyapunov functions, we verify the existence of a stationary distribution of the positive solution under the stochastic condition that R̂^{^}_s >1 and R^{^}_m >1. Furthermore, the explicit expression of probability density function around the quasi-endemic equilibrium is derived by solving the corresponding Fokker-Planck equation, which is guaranteed by the criteria R̂^{^}_s >1 and R̂^{^}_s > R^{^}_m. Finally, some numerical simulations are presented to verify the analytical results and a brief conclusion is drawn.