Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 497, Issue -, Pages 52-71Publisher
ELSEVIER
DOI: 10.1016/j.physa.2018.01.014
Keywords
Tuberculosis; Basic reproduction number; Backward bifurcation; Transcritical bifurcations; Hopf-bifurcation
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We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R-0 = 1. Our results demonstrate that the disease transmission rate beta and exogenous reinfection rate a plays an important role to change the qualitative dynamics of TB. The disease transmission rate beta give rises to the possibility of backward bifurcation for R-0 < 1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R-0 < 1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate beta and the exogenous reinfection rate alpha. We conducted some numerical simulations to support our analytical findings. (C) 2018 Published by Elsevier B.V.
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