Modeling the Dynamic of Herpes Simplex Virus II Incorporating Voluntary Laboratory Test and Medical Treatment

This study develops a mathematical model to investigate the transmission dynamics of HSV-II within the framework of symmetry in dynamical systems. The basic reproduction number ($R_0^{HSV}<1$) of the model was determined using the next generation method (NGM). The stability of the disease-free equilibrium point was also investigated using the Routh–Hurwitz Criterion and was found to be locally asymptotically stable (LAS) when $R_0^{HSV}<1$ but not globally asymptotically stable (GAS). To help ensure that the control variables were included correctly, sensitivity analysis was performed on the fundamental reproduction number parameters. Four control variables were applied for the model: HSV-II vaccination, effective condom use, laboratory test, and treatment. The optimality system was solved using Pontryagin’s maximum principle (PMP) to establish the optimal control strategy for combating the spread of the disease. Numerical solution was obtained by using the forward-backward Runge–Kutta fourth-order approach. The most effective approach to help eradicate HSV-II disease in the system is to combine the HSV-II vaccine, effective condom use, laboratory testing, and HSV therapy (strategy D).