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Stability analysis and optimal control of a vector-borne disease with nonlinear incidence

机译:具有非线性发生率的媒介传播疾病的稳定性分析和最优控制

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摘要

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive number R_0 and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.
机译:本文考虑了一种具有非线性发生率的媒介传播疾病传播动力学模型。事实证明,疾病的整体动力学完全由基本繁殖数决定。为了评估疾病控制措施的有效性,针对流行病学和人口统计学参数,提供了基本生殖数量R_0和地方流行比例的敏感性分析。根据敏感性分析的结果,对模型进行了修改,以评估三种控制措施的影响。预防性控制以尽量减少与媒介人类的接触,对感染者的治疗控制以及对媒介的杀虫剂控制。通过使用最优控制技术来分析确定最优控制的存在,并通过迭代方法在数值上解决该问题。模型的数值模拟和优化分析表明,限制和正确使用控制措施可能以可行的方式大大减少受感染的人数。

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