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.

霍乱是肠道的急性腹泻感染，其通过摄入被污染的水或食物而传播。这是一个重要的健康问题，尤其是在卫生条件差的县。本文采用最优控制理论对具有连续控制的霍乱动力学模型进行了理论研究。首先，使用埃塞俄比亚奥罗米亚地区霍乱的真实数据估算假定模型的参数。然后，对确定性霍乱模型的参数进行敏感性分析，以了解参数的相对重要性。可以观察到，从受感染的人类霍乱弧菌的吸入率（β ₂）和霍乱恢复率（γ）是最敏感的参数。然后将该系统扩展为一个最佳控制问题，以研究如何进行治疗和卫生，以减少感染和病原体的数量，同时将总实施成本降至最低。为此，我们设计了具有两个控件的控件功能：治疗和卫生。接下来，我们证明了系统存在最优控制。然后根据最优系统的解表示最优控制，然后证明了最优系统的唯一性。使用平均成本效益比和增量成本效益比进行比较，以检验最具有成本效益的策略。发现使用治疗作为对照是使用这两种方法的最具成本效益的策略。