A TB-HIV/AIDS coinfection model and optimal control treatment

Cristiana J. Silva; Delfim F. M. Torres

doi:10.3934/dcds.2015.35.4639

Article Contents

2015, Volume 35, Issue 9: 4639-4663. Doi: 10.3934/dcds.2015.35.4639

This issue Previous Article Fields of extremals and sensitivity analysis for multi-input bilinear optimal control problems Next Article Control of dynamical systems with discrete and uncertain observations

A TB-HIV/AIDS coinfection model and optimal control treatment

Cristiana J. Silva^1, and
Delfim F. M. Torres^2,

1.
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro
2.
CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro

Received: April 30, 2014

Revised: October 31, 2014

Published: May 2017

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Abstract

We propose a population model for TB-HIV/AIDS coinfection transmission dynamics, which considers antiretroviral therapy for HIV infection and treatments for latent and active tuberculosis. The HIV-only and TB-only sub-models are analyzed separately, as well as the TB-HIV/AIDS full model. The respective basic reproduction numbers are computed, equilibria and stability are studied. Optimal control theory is applied to the TB-HIV/AIDS model and optimal treatment strategies for co-infected individuals with HIV and TB are derived. Numerical simulations to the optimal control problem show that non intuitive measures can lead to the reduction of the number of individuals with active TB and AIDS.

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Mathematics Subject Classification: Primary: 92D30, 93A30; Secondary: 34D30, 49J15.

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