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Volume 4, Issue 1, 2026

Abstract

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Herpes simplex virus type 2 (HSV-2) is a persistent sexually transmitted infection (STI) with important public health implications, particularly among female sex workers (FSWs), where recurrent infection, asymptomatic shedding, and behavioral risk factors contribute to sustained transmission. This study develops a $\psi$-Hilfer fractional mathematical model for HSV-2 transmission dynamics to incorporate memory, hereditary effects, and nonlocal temporal dependence that cannot be fully captured by classical integer-order models. The proposed framework extends an existing HSV-2 transmission model by formulating the system with the $\psi$-Hilfer fractional derivative and analyzing its qualitative and numerical properties. We establish the existence, uniqueness, non-negativity, and boundedness of solutions within a biologically feasible region. The basic reproduction number is derived to characterize threshold behavior, and local and global stability analyses are performed for disease-free and endemic equilibria. In addition, an optimal control problem is formulated to evaluate prevention education, antiviral treatment, and behavioral intervention strategies. Necessary optimality conditions are obtained using fractional optimal control theory. Numerical simulations are carried out using the Adams–Bashforth–Moulton predictor–corrector method (ABM–PECE) under different fractional orders, type parameters, and kernel functions. The results demonstrate that the $\psi$-Hilfer fractional framework provides a flexible and biologically meaningful representation of HSV-2 persistence, delayed stabilization, and intervention response. Overall, the findings suggest that memory-based fractional modeling can improve predictive interpretation, stability characterization, and control design for HSV-2 transmission, especially in high-risk populations where historical exposure and recurrent infection play central roles.

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