Healthcare Analytics (Nov 2023)
Effective strategies towards eradicating the tuberculosis epidemic: An optimal control theory alternative
Abstract
The efforts to eradicate tuberculosis (TB) globally has been on-going for over decades, though the world is yet to be free from the disease. This, possibly, necessitated the inclusion of the health target to wipe-off the disease from the world by the year 2030 in the United Nations Sustainable Development Goals (SDG). Here, we used a deterministic model to capture the disease transmission dynamics and formulated the SDG as an optimal control problem subject to the disease dynamics model incorporating three time-dependent control variables, namely, vaccination, treatment for actively infected individuals without drug resistance, and treatment for the actively infected individuals with drug resistance. Based on Pontryagin’s maximum principle, we derived the problem’s optimality system and solved the resulting system numerically to investigate the effects of using at least any one of the three control measures on the dynamics of TB. Findings from the simulations of our results were discussed. Furthermore, efficiency and cost-effectiveness analyses were conducted to reveal the most efficient and most cost-effective single, double and triple interventions needed to prevent and control the spread of TB in the population with limited resources. The study recommends that the intervention strategy which combines all the controls is the most efficient strategy that can be implemented to reduce the spread of TB significantly in the population when the resources are available. In resource-limited communities, single application of optimal vaccination and combination of optimal vaccination and treatment control for actively infected individuals without drug resistance are the alternative intervention strategies that can be implemented to effectively manage the burden of TB in the population.
