Dwi Lestari, Noorma Yulia Megawati, Nanang Susyanto, Fajar Adi-Kusumo, Karam Allali
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 ((Formula presented.) and (Formula presented.)) was computed, revealing that the disease dies out whenever (Formula presented.) and (Formula presented.). 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. © 2025 John Wiley & Sons Ltd.
Department of Mathematics Education, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia; Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia; Laboratory of Mathematics, Computer Science, and Applications, Faculty of Sciences and Technology, Hassan II University of Casablanca, Mohammedia, Morocco
