Transmission Model for the Co-infection of HIV/AIDS and Tuberculosis

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Authors

  • Carla MA Pinto Department of Mathematics, School of Engineering, Polytechnic of Porto, and Center of Mathematics, University of Porto, and GECAD - Knowledge Engineering and Decision Support Research Center Rua Dr António Bernardino de Almeida, 431, 4200-072 Porto, PORTUGAL Author
  • Ana Carvalho Department of Mathematics, Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, 4440–452 Porto, Portugal Author

DOI:

https://doi.org/10.5890/JAND.2014.03.006

Abstract

A mathematical model for the dynamics of co-infection of HIV/AIDS and tuberculosis is developed. The model includes treatment for both HIV and tuberculosis and vertical transmission for HIV/AIDS. The disease-free equilibrium of the model is computed and its local stabil- ity is proved. The reproduction numbers of the full model and of its two submodels, the HIV only model and the TB only model, are also calculated. Numerical simulations show the disease-free equilibrium. Future work will focus on computing the stability of the endemic equilibria.

References

[1] Naresh, R. and Tripath A. (2005), Modelling and analysis of HIV-TB co-infection in a variable size population, Mathematical Modelling and Analysis , 10, 275-286.

[2] World Health Organization (2012). TB/HIV. http://www.who.int/gho/publications/world$_$health$_ $statistics/EN$_$WHS2012$_$Full.pdf.

[3] Bhunu, C.P., Garira, W., and Mukandavire Z. (2009), Modeling HIV/AIDS and Tuberculosis Coinfection, Bulletin of Mathematical Biology, 71, 1745-1780.

[4] Waziri, A.S., Massawe, E.S., and Makinde, O.D. (2012), Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical Transmission, Applied Mathematics, 2, 77-89.

[5] Driessche, P. and Watmough, P. (2002), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48.

[6] Dye, C. and William, G.P. (2000), Criteria for the control of drug-resistant tuberculosis, Proceedings of the National Academy of Sciences, 97, 8180-8185.

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PublishedMarch 2014

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 3 No. 1 (2014): Regular Issue

Section

Research Articles

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Unless an article landing page states a Creative Commons or other article-specific license, the article is published by L&H Scientific Publishing, LLC and all rights are reserved. The article-level license and copyright notice govern access and reuse.

How to Cite

Pinto, C. M., & Carvalho, A. (2026). Transmission Model for the Co-infection of HIV/AIDS and Tuberculosis. Journal of Applied Nonlinear Dynamics, 3(1), 73-84. https://doi.org/10.5890/JAND.2014.03.006

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