Deterministic and stochastic model for the hepatitis C with different types of virus genome

In this paper, a deterministic and stochastic model for hepatitis C with different types of virus genomes is proposed and analyzed. Some sufficient conditions are obtained to ensure the stability of the deterministic equilibrium points. We perform a stochastic extension of the deterministic model to study the fluctuation between environmental factors. Firstly, the existence of a unique global positive solution for the stochastic model is investigated. Secondly, sufficient conditions for the extinction of the hepatitis C virus from the stochastic system are obtained. Theoretical and numerical results show that the smaller white noise can ensure thepersistence of susceptible and infected populations while the larger whitenoise can lead to the extinction of disease. By introducing the basic reproduction number $R_0$ and the stochastic basic reproduction number $R_0^s$, the conditions that cause the disease to die out are indicated. The importance of environmental noise in the propagation of hepatitis C viruses is highlighted by these findings.