Abstract
This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward–Backward Sweep method in the Matlab programme. The numerical results revealed that the combination of all optimal control measures is the most effective strategy for minimizing the spread and impact of disease in the community. Furthermore, a cost-effectiveness analysis was performed to determine the most cost-effective strategy using the incremental cost-effectiveness ratio approach and we observed that the rodenticide control-only strategy is most effective to combat the spread of disease when available resources are limited.
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