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Mathematical epidemiology of HIV/AIDS and tuberculosis co-infection

University of British Columbia

The project deals with the analysis of a general dynamical model for the spread of HIV/AIDS and tuberculosis Co-infection. We capture in the model the dynamics of HIV/AIDS infected individuals and investigate their impacts in the progression of tuberculosis with and without TB treatment. It is shown that TB-only model and HIV-only model have locally asymptotically stable disease-free equilibrium when the basic reproduction number is less than unity and a unique endemic equilibrium exists when the basic reproduction number is greater than unity. We analyze the full HIV/AIDS-TB coinfection model and incorporate treatment strategy for the exposed and active forms of TB. The stability of equilibria is derived through the use of Van den Driessche method of generational matrix and Routh Harwitz stability criterion. Numerical simulations are provided to justify the analytical results and to investigate the effect of change of certain parameters on the co-infection. Sensitivity analysis shows that reducing the most sensitive parameters β₁ and β₂ could help to lower the basic reproduction number and thereby reducing the rate of infection. From the study, we conclude that treating latent and active forms of TB reduce the rate of infection, reduce the rate of progression of individuals to AIDS stage and lowers co-infection.

Text

2015-08-05

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54295

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/