Fuzzy Logic–Integrated Optimal Control for Dynamic Intervention in Hepatitis C Virus Epidemiology

Hepatitis C Virus (HCV) continues to be a significant worldwide health issue, particularly in resource-limited environments with inadequate diagnostic and therapeutic options. This study formulates a deterministic six-compartment model, predicated on the assumptions that the population undergoes natural birth-death dynamics, awareness initiatives transition individuals from $S_1$ to $S_2$, diagnosis advances U to I, recovery is achieved through therapy or immunity, and infection and mortality rates vary among classes. The system is described by coupled nonlinear ODEs that include three time-dependent controls. Analytical examination guarantees the positivity and boundedness of all compartments and calculates the fundamental reproduction number ($R_0$) using the next-generation matrix. Sensitivity analysis shows that $\beta_1, \beta_2, \tau_1, \tau_2$ are the most important parameters. Using Pontryagin's Maximum Principle, the forward–backwards sweep method is employed to determine the optimal controls that minimise both infection and cost. A Mamdani fuzzy logic controller is added to handle parameter uncertainty and generate adaptive responses to infection pressure, awareness level, and hospital load. Simulations reveal that fuzzy control delivers equivalent suppression to the crisp optimum with around two-thirds lower cost, enabling a stable, interpretable, and resource-efficient paradigm for dynamic HCV intervention.