On the Optimal Control of HIV-TB Co-Infection and Improvement of Workplace Productivity

Human immunodeficiency virus (HIV) and tuberculosis (TB) have long been known to have a synergistic relationship. This is a result of each of the diseases impacting negatively on the immune system of the infected persons. The impact of these diseases on workforce productivity is studied in this paper from the viewpoint of dynamical systems. In this paper, we present a nonlinear ordinary differential equation model to study the dynamics of HIV-TB co-infection and its effect on workforce productivity. The main model is first decoupled into two basic submodels of HIV-only and TB-only models, whose qualitative properties are presented before the qualitative properties of the main model are studied. While the HIV-only model is shown to have a globally asymptotically stable disease-free equilibrium whenever its basic reproduction number is less than unity, the TB-only model is shown to exhibit backward bifurcation under some conditions. To investigate the impact of various intervention strategies on the control of the co-infection and improvement of workforce productivity, five time-dependent controls (involving transmission prevention for the two diseases, therapy for the two diseases, and capacity building for improved workforce productivity) are incorporated into the basic model to form an optimal control problem, which is qualitatively analyzed using Pontryagin's maximum principle and numerically simulated. Incremental cost-effectiveness analysis is conducted with the results of the numerical simulations. It is observed that the most cost-effective strategy for fighting the spread of the co-infection with enhanced productivity is that of combining both preventative and curative measures along with skills training.