Dynamics of HSV-2 in the presence of optimal counseling and education among prisoners (Q2045342)

Summary: Herpes simplex virus type 2 (HSV-2) is one of the major sexually transmitted infections in sub-Saharan prisons and the major driver of HIV. In this paper, we propose and analyze a basic mathematical model for the spread of HSV-2 in prisons. We compute the basic reproduction number and demonstrate that it is a sharp threshold for disease dynamics. The impacts of counseling and education of HSV-2-infected individuals are examined. Equilibrium states of the model are determined and their stability is investigated. The basic model is then extended to incorporate a time-dependent intervention strategy. The aim of the control is tied to reducing the number of infectious individuals through early detection, education, and counseling of the infected. The Pontryagin's Maximum Principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically.