A Stochastic Hepatitis C Epidemic Model in Cellular Level With a Lévy Noise

ABSTRACT In this paper, we deal with a Lévy noise‐driven epidemic model reflecting the dynamics of hepatitis C virus infection subject to the effect of the immune cells. A stochastic model for hepatitis C at the cellular level is developed, considering random fluctuations and the influence of immune cells. After formulating the model, the system's feasibility was examined using the fundamental principles of existence and uniqueness theory. Additionally, the behavior of the solutions near the disease‐free and endemic equilibrium points was analyzed. To evaluate the persistence or elimination of the infection, the threshold parameter a reproduction number ( and ) was computed, revealing that the disease dies out whenever and . Numerical simulations are performed to illustrate the analysis results. Finally, we establish the stochastic stability of the disease‐free equilibrium point. We examine stochastic disease extinction. Furthermore, we have demonstrated that the disease persists with or without immunity under appropriate conditions. Numerical simulations have been performed to confirm the theoretical results and demonstrate the stochastic dynamics of infection.