In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

中文翻译：

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具有时间依赖性控制的埃博拉感染的确定性流行病模型

在本文中，我们使用非线性常微分方程和最优控制理论研究了埃博拉病毒感染的流行病学模型。我们考虑了针对致命埃博拉病毒感染的SIR和SEIR模型的最佳控制分析，方法是使用疫苗接种，治疗和教育运动作为随时间变化的控制功能。我们已应用间接方法来研究现有的针对埃博拉病毒病的确定性最佳控制流行病模型。这些最优控制方法是基于哈密顿函数和庞特里亚金的最大原理来构造伴随方程和最优系统。使用四阶Runge-Kutta方法进行的前-后扫描数值方案用于求解各种控制策略的最优系统。从我们的数字插图，