Optimal Control of Exogenous Reinfection Prevention and Treatment on a Tuberculosis Model

Zainullah Zuhri, Abdulloh Hamid, Subchan, Imam Rofiki

2018

Abstract

We apply optimal control for a system of ordinary differential equations in modelling tuberculosis disease with exogenous reinfection. Reducing the contact between exposed and infectious tuberculosis people and increasing the population of the medication compartment can be done to overcome the spreading of tuberculosis disease. We use control strategy of the tuberculosis disease to represent the prevention of exogenous reinfection and optimal treatment. Using Pontryagin’s maximum principle, we have discussed optimal control of the tuberculosis disease. We use Forward-Backward Sweep Method to gain optimal system numerically. Numerical results show that the performance of 2-control model is highly effective for reducing the number of infected individuals in the Tuberculosis model by considering the simulation results from Susceptible, Exposed, Infectious and Treated population satisfying from each expected condition.

Paper Citation

in Harvard Style

Zuhri Z., Hamid A., Subchan. and Rofiki I. (2018). Optimal Control of Exogenous Reinfection Prevention and Treatment on a Tuberculosis Model. In Proceedings of the Built Environment, Science and Technology International Conference - Volume 1: BEST ICON, ISBN 978-989-758-414-5, pages 235-239. DOI: 10.5220/0008904700002481

in Bibtex Style

@conference{best icon18,
author={Zainullah Zuhri and Abdulloh Hamid and Subchan and Imam Rofiki},
title={Optimal Control of Exogenous Reinfection Prevention and Treatment on a Tuberculosis Model},
booktitle={Proceedings of the Built Environment, Science and Technology International Conference - Volume 1: BEST ICON,},
year={2018},
pages={235-239},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008904700002481},
isbn={978-989-758-414-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the Built Environment, Science and Technology International Conference - Volume 1: BEST ICON,
TI - Optimal Control of Exogenous Reinfection Prevention and Treatment on a Tuberculosis Model
SN - 978-989-758-414-5
AU - Zuhri Z.
AU - Hamid A.
AU - Subchan.
AU - Rofiki I.
PY - 2018
SP - 235
EP - 239
DO - 10.5220/0008904700002481