Optimal Control Strategies and Cost-effectiveness Analysis Applied to Real Data of Cholera Outbreak in Ethiopia’s Oromia Region

Abstract

Abstract Cholera is an acute, diarrheal infection of the intestine which spreads by the ingestion of contaminated water or food. It is an important health problem, especially in counties with poor sanitation and hygiene. In this paper, the Cholera dynamics model with continuous controls is theoretically investigated using optimal control theory. First, the parameters of the assumed model are estimated using a real data of Cholera from Ethiopia’s Oromia Region. Then the sensitivity analyses of the parameters of the deterministic Cholera model is investigated to see the relative importance of parameters. It is observed that the intake rate of Vibrio Cholerae from infected humans (β2) and the cholera recovery rate (γ) are the most sensitive parameters. The system is then extended into an optimal control problem to investigate how treatment and sanitation should be carried out to reduce the number of infected and pathogenic populations while minimizing the total cost of implementation. To this end, we have designed a control functional having two controls: treatment and sanitation. Next, we have shown that the optimal controls exist for the system. Then the optimal controls are represented in terms of the solutions of the optimality system, and then the uniqueness of the optimality system is proved. The average cost-effectiveness ratio and the incremental cost-effectiveness ratio are used and compared to examine the most cost-effective strategy. The use of treatment as control is found out to be the most cost-effective strategy using both methods.