A new mathematical model is formulated to investigate the transmission dynamics of cholera under vaccination, with a focus on the impact of vaccination age. The basic reproduction number is derived and proved to be a sharp control threshold determining whether or not the infection is persistent. We conduct a rigorous analysis on the local and global stability properties of the equilibria in system. Meanwhile, we compare the results to those of the simplified model based on ordinary differential equations where the effects of vaccination age are not incorporated. Numerical simulation results verify our analytical findings.

中文翻译：

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霍乱传播动力学与疫苗接种年龄的建模和分析

制定了一个新的数学模型来研究接种疫苗时霍乱的传播动态，重点是疫苗接种年龄的影响。推导出基本繁殖数并证明它是确定感染是否持续的严格控制阈值。我们对系统平衡的局部和全局稳定性进行了严格的分析。同时，我们将结果与基于常微分方程的简化模型的结果进行比较，其中不包括疫苗接种年龄的影响。数值模拟结果验证了我们的分析结果。