Control of The Spread of TB-HIV/AIDS Coinfection Using Optimal Control

  • Yuyun Monita UIN Sunan Ampel Surabaya, Surabaya, Indonesia
  • Putroue Keumala Intan UIN Sunan Ampel Surabaya, Surabaya, Indonesia
Keywords: TB-HIV/AIDS coinfection, Pontryagin, Fourth order Runge-Kutta

Abstract

The condition in which an individual is affected by TB and HIV/AIDS in his body is called a TB-HIV/AIDS coinfection. This research aims to minimize the populations of TB-HIV/AIDS coinfection with a minimum expenditure on medical expenses, that means minimizing the objective’s function ( ) or purpose function. In this research, modification of the model was carried out by adding the treatment population for HIV patients with ARV ( ). The population used was 11 classes with the use of three controls including treatment for individuals with latent TB ( ), active TB ( ), and HIV ( ). After performing numerical simulation using the forward backward fourth order Runge-Kutta, the results show that scenario 7 is the best scenario in controlling the spread of TB-HIV/AIDS coinfection because it resulted a minimum  value of 1401,44. This means that providing the treatment for individuals with latent TB, active TB, and HIV in tandem can reduce the populations of TB-HIV/AIDS coinfection in the minimum treatment cost.

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CROSSMARK
Published
2021-05-31
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How to Cite
MonitaY., & Keumala IntanP. (2021). Control of The Spread of TB-HIV/AIDS Coinfection Using Optimal Control. Jurnal Matematika MANTIK, 7(1), 96-106. https://doi.org/10.15642/mantik.2021.7.1.96-106