We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.

中文翻译：

---

在疾病控制措施下模拟霍乱传播

我们提出了一个新的数学模型来研究霍乱在疾病控制措施下的传播动态，包括教育计划和水卫生。该模型将教育计划的影响纳入疾病传播率，将水卫生的影响纳入环境病原体动态。我们对模型的自治系统进行了详细分析，并建立了其平衡的局部和全局稳定性，该平衡表征了霍乱的阈值动态。然后，我们对具有时间相关控制的一般模型进行优化控制研究，并探索实施教育计划和水卫生的有效方法，同时平衡其成本。