Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Nayeem, Jannatun and Sultana, Israt (2019) Mathematical Analysis of the Transmission Dynamics of Tuberculosis. American Journal of Computational Mathematics, 09 (03). pp. 158-173. ISSN 2161-1203

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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.

Item Type: Article
Subjects: Digital Open Archives > Mathematical Science
Depositing User: Unnamed user with email support@digiopenarchives.com
Date Deposited: 15 Jun 2023 07:57
Last Modified: 28 May 2024 05:30
URI: http://geographical.openuniversityarchive.com/id/eprint/1461

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