Investigation of an optimal control strategy for a cholera disease transmission model with programs - Alemneh, Haileyesus Tessema; Teklu, Shewafera Wondimagegnhu; Kotola, Belela Samuel; Mekonen, Kassahun Getnet (Frontiers in Applied Mathematics and Statistics, 2024)
In this paper, an optimal control deterministic mathematical model of cholera disease with costeffectiveness analysis is developed and analyzed considering direct and indirect contact transmission pathway. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis on the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Under the implementation of Pontryagin's maximum principle, characterization of the optimal controls optimality system system is established. The numerical simulation results on the integrated control strategies are demonstrated that strategy 2 ,7 and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, government stakeholders and policymakers were advised by the research findings to execute any one of the three integrated intervention programs.