Modeling, optimal control of intervention strategies and cost effectiveness analysis for buruli ulcer model

Abstract

Abstract A mathematical model for the transmission of buruli ulcer disease is proposed in this paper, incorporating three control strategies. Using the stability theory of differential equations, optimal control, and computer simulation, a nonlinear mathematical model for the problem is developed and qualitatively analyzed. Buruli ulcer free equilibrium and buruli ulcer present equilibrium were established. Using the next-generation operator method, the basic reproduction number of the model is obtained. It is found that the buruli ulcer-free equilibrium point is asymptotically stable locally and globally when R 0 1 and otherwise when R 0 > 1 . The bifurcation analysis performed in this study indicates that the buruli ulcer model exhibits backward bifurcation. To investigate the parameters that influence the basic reproduction number R 0 , sensitivity analysis is performed. To minimize the transmission dynamics of buruli ulcer in humans and water bugs populations respectively, the buruli ulcer model is updated to include control measures attached to the parameters that affect the R 0 . In particular, the prevention measures covered are health education on the use of protective clothing, treatment of infected humans, and spraying of insecticides. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. Using forward and backward sweep techniques in MATLAB, the optimality system was solved numerically. The results of the simulations show that, relative to the case of no control, there is a substantial decrease in the population of infected humans and the total population of water bugs when control measures are implemented. A study of cost-effectiveness shows that the most cost-effective approach is strategy G with the smallest ICER of 33442.44. To mitigate or eliminate buruli ulcer in the population, we conclude that the government should invest in health education on the use of protective clothing, treatment of infected humans, and the use of insecticide spray.