Modeling optimal control strategies for HIV and gonorrhea co-infection: incorporating screening along with treatment

Abstract Human immunodeficiency virus (HIV) and gonorrhea are significant infectious diseases that pose considerable public health challenges worldwide. In this study, a control-induced model is developed to explore the dynamics of HIV and gonorrhea co-infection in the presence of treatment, incorporating screening strategies as control variables. We establish qualitative behavior, such as nonnegativity and boundedness of the solutions, and compute the basic reproduction number by utilizing the next generation matrix method. Subsequently, the stability of the disease-free equilibrium is analyzed, and then sensitivity analysis is undertaken to pinpoint the most critical parameters. Furthermore, an optimal control problem is formulated to diminish the total count of infected individuals and associated costs. The existence of an optimal control is shown, and Pontryagin’s principle is employed to derive the necessary conditions for an optimality system. Additionally, numerical simulations reveal that without control measures, the model predicts a continual rise in the number of infections. However, the graphical results demonstrate that the simultaneous implementation of screening for both HIV and gonorrhea as control measures significantly reduces single infections as well as co-infections. These insights are vital for researchers and policymakers to develop effective intervention strategies for eradicating co-infections of HIV and gonorrhea.