Stochastic Modeling and Optimal Decision-Making for an Imprecise HCV System Under Treatment

Hepatitis C virus (HCV) is a major global health concern caused by a blood-borne viral infection that primarily targets the liver. Due to the difficulty of obtaining accurate parameter estimates in epidemiological systems, we incorporate parameter uncertainty into the modeling framework by means of a stochastic imprecise differential system. In this work, we investigate a treatment strategy for an HCV stochastic model under environmental fluctuations and parameter imprecision. We establish the existence and positivity of the global solution. By using Lyapunov function techniques and stochastic stability theory, we derive sufficient conditions for both extinction and persistence of the disease, expressed in terms of a stochastic threshold [Formula: see text]. Furthermore, we formulate a near-optimal control problem in a non-convex control setting and obtain a priori estimates for admissible controls. By applying Ekeland’s variational principle together with the stochastic Hamiltonian maximum condition, we derive necessary and sufficient conditions for near-optimality of the control problem. Finally, numerical simulations are provided to illustrate and support the theoretical results.