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An Optimal Treatment Control of TB-HIV Coinfection

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  • Fatmawati
  • Hengki Tasman

Abstract

An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments.

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  • Fatmawati & Hengki Tasman, 2016. "An Optimal Treatment Control of TB-HIV Coinfection," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-11, March.
    • Handle: RePEc:hin:jijmms:8261208
    DOI: 10.1155/2016/8261208
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    Cited by:

    1. Salman, Mohammad & Das, Ruchi, 2018. "Multi-sensitivity and other stronger forms of sensitivity in non-autonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 341-348.
    2. Fatmawati & Endrik Mifta Shaiful & Mohammad Imam Utoyo, 2018. "A Fractional-Order Model for HIV Dynamics in a Two-Sex Population," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-11, April.

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