In this article, we study the control of a Chikungunya epidemic model solving several optimal control problems. We implement three strategies to control the spread of the Chikungunya virus in the human and vector population. The first control strategy is an educational campaign promoting the use bednets, avoiding water stagnation, wearing long sleeved shirts, among others. The second is treatment of the infected individual, and the third relies on spraying insecticide. The optimal control problem that we solve has a mathematical model for Chikungunya representing the control system. We rely on Pontryagin's maximum principle to solve the optimal control problem. For the mathematical model of the Chikungunya epidemic, we use the incidence data from Colombia corresponding to the year 2015. An additional aim of this study is to investigate which control measures are more efficient and suggest policies to health institutions to reduce the number of infected individuals. Although the mathematical model fits real data of the Colombian case, the policies and insights presented in this article might be extrapolated to different countries.

中文翻译：

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使用最佳控制设计基孔肯雅流行公共卫生政策的数学模型

在本文中，我们研究了解决几个最优控制问题的基孔肯雅病流行模型的控制。我们实施三种策略来控制基孔肯雅病毒在人类和媒介人群中的传播。第一个控制策略是开展教育运动，以促进使用蚊帐，避免水停滞，穿长袖衬衫等。第二种是对感染者的治疗，第三种是喷洒杀虫剂。我们解决的最优控制问题具有代表控制系统的Chikungunya数学模型。我们依靠庞特里亚金的最大原理来解决最优控制问题。对于基孔肯雅流行的数学模型，我们使用了哥伦比亚对应于2015年的发病率数据。这项研究的另一个目的是研究哪种控制措施更有效，并向卫生机构提出减少感染个体数量的政策建议。尽管数学模型适合哥伦比亚案例的真实数据，但本文中介绍的政策和见解可能会推断到不同的国家。