As a zoonotic disease, leptospirosis has now been identified as one of the emerging infectious diseases. In this paper, we analyze the propagation of leptospirosis and find a schedule for control programs to eradicate the disease in a cattle ranch. A mathematical model has been built with ordinary differential equations (ODEs) to understand the epidemiology of leptospirosis and main factors on its transmission. We investigated the disease free equilibrium of the model and its stability using the basic reproduction number, ℛ0, and target reproduction number, 𝒯𝒮. Then, the model incorporates vaccination and recruitment control programs in the form of impulse actions as measures to prevent the propagation of leptospirosis in the ranch. Parameter estimation and sensitivity analysis are presented as a part of this study.

中文翻译：

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家畜牛钩端螺旋体病具有冲动作用的年龄结构模型

作为一种人畜共患病，钩端螺旋体病现已被确定为新兴传染病之一。在本文中，我们分析了钩端螺旋体病的传播，并找到了控制计划的时间表，以根除牛场中的疾病。使用常微分方程 (ODE) 建立了一个数学模型，以了解钩端螺旋体病的流行病学及其传播的主要因素。我们使用基本再生数研究了模型的无病平衡及其稳定性，ℛ0, 和目标再生数,𝒯𝒮. 然后，该模型将疫苗接种和招募控制计划以脉冲行动的形式作为防止钩端螺旋体病在牧场传播的措施。参数估计和敏感性分析是本研究的一部分。