Optimal Treatment Strategies for Tuberculosis with Exogenous Reinfection

Tuberculosis (TB) is a disease found in about one third of the world population. There is some controversy on the role of exogenous reinfection; with some epidemiologists supporting it while others consider it irrelevant. However, even at a minimal level, the presence of exogenous reinfection is capable of generating hysteresis and supporting multiple endemic states when the basic reproduction number (R0) is less than one. In this manuscript, we study the use of control in areas where TB is prevalent (R0 > 1) as well as in areas where some additional effort (R0 < 1) may be able to eliminate the disease. In this model, controls on social distancing, disease relapse, and treatment are incorporated to reduce the latently infected and actively infected populations, via the application of optimal control theory.