Mathematical Analysis of the Transmission Dynamics of Tuberculosis
Open Access
- 1 January 2019
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in American Journal of Computational Mathematics
- Vol. 09 (03), 158-173
- https://doi.org/10.4236/ajcm.2019.93012
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.Keywords
This publication has 11 references indexed in Scilit:
- Global Stability of SIR and SEIR Model for Tuberculosis Disease Transmission with Lyapunov Function MethodAsian Journal of Applied Sciences, 2016
- A Mathematical study on the vaccination impact on the disease dynamics of HBVIOSR Journal of Mathematics, 2014
- Treatment interruptions and duration associated with default among new patients with tuberculosis in six regions of RussiaInternational Journal of Infectious Diseases, 2009
- Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatmentMathematical Biosciences and Engineering, 2008
- Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosisMathematical Biosciences and Engineering, 2008
- Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in NigeriaMathematical Modelling of Natural Phenomena, 2007
- Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmissionJournal of The Royal Society Interface, 2006
- Strategies for mitigating an influenza pandemicNature, 2006
- A Two-Strain Tuberculosis Model with Age of InfectionSIAM Journal on Applied Mathematics, 2002
- The intrinsic transmission dynamics of tuberculosis epidemicsNature Medicine, 1995