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Journal of Applied Nonlinear Dynamics 3(1) (2014) 73--84 | DOI:10.5890/JAND.2014.03.006

Carla MA Pinto$^{1}$; Ana Carvalho$^{2}$

1Department 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

2Department of Mathematics, Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, 4440–452 Porto, Portugal

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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.

Acknowledgments

Authors which to thank Fundação Gulbenkian, through Prémio Gulbenkian de Apoio à Investigação 2003, and the Polytechnic of Porto, through the PAPRE Programa de Apoio à Publicação em Revistas Científicas de Elevada Qualidade for financial support.

References

1. [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. [2]	World Health Organization (2012). TB/HIV. http://www.who.int/gho/publications/world$_$health$_ $statistics/EN$_$WHS2012$_$Full.pdf.

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

4. [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. [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. [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.