Taiwanese Journal of Mathematics

A MATHEMATICAL MODEL WITH OPTIMAL CONTROLS FOR CELLULAR IMMUNOLOGY OF TUBERCULOSIS

Ruiqing Shi, Yang Li, and Sanyi Tang

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Abstract

In this paper we propose a system of ordinary differential equations to model the interaction among non-infected macrophages, infected macrophages, T cells and Mtb bacilli. Model analysis reveals the existence of infection-free equilibrium and the endemically infected equilibrium. And we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss a quadratic control and a linear control. The quadratic control allows for a weaker treatment that more effectively than the linear control.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 575-597.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706403

Digital Object Identifier
doi:10.11650/tjm.18.2014.3739

Mathematical Reviews number (MathSciNet)
MR3188520

Zentralblatt MATH identifier
1357.92047

Subjects
Primary: 34H05: Control problems [See also 49J15, 49K15, 93C15] 49J15: Optimal control problems involving ordinary differential equations

Keywords
optimal controls mycobacterium tuberculosis equilibrium singular arc

Citation

Shi, Ruiqing; Li, Yang; Tang, Sanyi. A MATHEMATICAL MODEL WITH OPTIMAL CONTROLS FOR CELLULAR IMMUNOLOGY OF TUBERCULOSIS. Taiwanese J. Math. 18 (2014), no. 2, 575--597. doi:10.11650/tjm.18.2014.3739. https://projecteuclid.org/euclid.twjm/1499706403


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