Stochastic optimal analysis for the hepatitis B epidemic model with Markovian switching

A new stochastic epidemic model is introduced, explaining the dynamics of hepatitis B with the inclusion of white noise, Markovian switching, and vaccination control. In this research, we prove the existence of a unique global positive solution for the model. We also formulated an appropriate "stochastic Lyapunov" operator and used the "Khasminskii" approach to prove that the model has unique stationary distribution. The extinction of the model is also investigated. We study an optimal control problem for the stochastic model. Finally, the numerical experiments are presented to illustrate the obtained results.