Optimal control of viral infection model with saturated infection rate

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI:10.3934/naco.2020031

J. Danane

引用次数: 2

Abstract

This paper deals with an optimal control problem for a viral infection model with cytotoxic T-lymphocytes (CTL) immune response. The model under consideration describes the interaction between the uninfected cells, the infected cells, the free viruses and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin's maximum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity.

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饱和感染率下病毒感染模型的最优控制

研究具有细胞毒性t淋巴细胞(CTL)免疫应答的病毒感染模型的最优控制问题。所考虑的模型描述了未感染细胞、感染细胞、游离病毒和CTL细胞之间的相互作用。这两种治疗方法代表了药物治疗在抑制病毒产生和预防新感染方面的效率。建立了最优控制对的存在性，并利用庞特里亚金极大值原理对这两个最优控制进行了表征。利用正、后向差分逼近法推导了最优系统，并对其进行了数值求解。最后，进行了数值模拟，以显示最佳治疗在控制感染严重程度中的作用。

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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来源期刊

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.