In this paper, we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human community. Firstly, we combined a model of Vibrio Cholerae with a generic SIRS cholera model. Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations. Then we presented the theoretical analysis of the model. More precisely, we computed the disease free equilibrium. We derive the basic reproduction number [Formula: see text] which determines the extinction and the persistence of the infection. We show that the trivial disease-free equilibrium is globally asymptotically stable whenever [Formula: see text], while when [Formula: see text], the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. Theoretical results are supported by numerical simulations, which further suggest that the control of cholera should consider both sensitization and sanitation, with a strong focus on the latter.

中文翻译：

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具有控制作用的周期性环境中的霍乱数学模型

在本文中，我们研究了宣传和卫生作为可能的控制措施的影响，以减少人类社区内霍乱流行的传播。首先，我们将霍乱弧菌模型与通用 SIRS 霍乱模型相结合。通过脉冲微分方程整合了人口和卫生敏感性方面的经典控制策略。然后我们对模型进行了理论分析。更准确地说，我们计算了无病平衡。我们推导出基本繁殖数[公式：见正文]，它决定了感染的灭绝和持续存在。我们证明，当 [公式：见文本] 时，平凡无病平衡是全局渐近稳定的，而当 [公式：见文本] 时，平凡的无病平衡是不稳定的，并且存在一个全局渐近稳定的独特的地方病平衡点。理论结果得到数值模拟的支持，这进一步表明霍乱的控制应同时考虑致敏和卫生，重点关注后者。