Optimal singular controls for VSEIR model of Tuberculosis

M. S. Sinaga, Y. Rangkuti
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Abstract

The optimality singular controls of a VSEIR model of Tuberculosis are analyzed in this paper. There are controls that correspond to time- vary the vaccination and treatment schedules. A Hamiltonian (H) of the model is defined. The model is splited into separate one-dimensional problems, the so-called switching functions. The extreme occurs when a switching function disappears suddenly over an open interval. In which the derivatives of switching function must disappears suddenly and this typically allows computing such a control. The second-order of the function is not vanishing, which satisfied Legendre-Clebsh condition, and thus the controls of these kinds are called singular. In this work, our main emphasis is on a complete analysis of the optimum properties corresponding to trajectories. The result shows that vaccination control is singular, but treatment is not. This means that the model reached the optimality control for vaccination schedule, but not treatment schedule.
结核病VSEIR模型的最优奇异控制
本文分析了结核VSEIR模型的最优奇异控制问题。有相应于时间变化的疫苗接种和治疗计划的控制。定义了模型的哈密顿量H。该模型被分割成独立的一维问题,即所谓的切换函数。当开关函数在一个开放间隔内突然消失时,就会出现极端情况。其中开关函数的导数必须突然消失,这通常允许计算这样的控制。函数二阶不消失,满足legende - clebsh条件,因此这类控制被称为奇异控制。在这项工作中,我们的主要重点是对与轨迹相对应的最佳特性的完整分析。结果表明,预防接种控制是单一的,而治疗不是单一的。这意味着该模型达到了疫苗接种计划的最优控制,但没有达到治疗计划的最优控制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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