Affiliation:
1. College of Business Education (CBE), Postal Address Box 1968, Dar es Salaam, Tanzania
2. Mathematics Department, University of Dar es Salaam, Postal Address Box 35065, Dar es Salaam, Tanzania
Abstract
An optimal control model of African trypanosomiasis to minimize the cost of implementing control efforts and the number of infected humans, cattle, and tsetse-fly populations in their respective communities was formulated. Time-dependent controls such as public health education, human and cattle treatments, and tsetse-fly trapping were considered. Using Pontryagin’s maximum principle, the necessary conditions and the existence of an optimal control solution of an optimal control problem were analyzed. Using forward and backward in time fourth-order Runge–Kutta scheme, numerical simulations of the optimal control problem were performed. The results showed that the strategy involving public health education, treatment of humans, cattle treatment, and trapping of tsetse-flies was the most effective in reducing the number of infected individuals in their respective populations. Furthermore, the incremental cost-effectiveness analysis was performed, which showed that the tsetse-fly trapping was the most cost-effective strategy to implement in source limited settings.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology,Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology