American Journal of Computational Mathematics

Volume 9, Issue 3 (September 2019)

ISSN Print: 2161-1203   ISSN Online: 2161-1211

Google-based Impact Factor: 1.05  Citations  

Mathematical Analysis of the Transmission Dynamics of Tuberculosis

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DOI: 10.4236/ajcm.2019.93012    1,249 Downloads   3,647 Views  Citations

ABSTRACT

We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.

Share and Cite:

Nayeem, J. and Sultana, I. (2019) Mathematical Analysis of the Transmission Dynamics of Tuberculosis. American Journal of Computational Mathematics, 9, 158-173. doi: 10.4236/ajcm.2019.93012.

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