Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation

Subhas Khajanchi, Dhiraj Kumar Das and Tapan Kumar Kar

Physica A: Statistical Mechanics and its Applications, 2018, vol. 497, issue C, 52-71

Abstract: 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 R0=1. Our results demonstrate that the disease transmission rate β and exogenous reinfection rate α plays an important role to change the qualitative dynamics of TB. The disease transmission rate β give rises to the possibility of backward bifurcation for R0<1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R0<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 β and the exogenous reinfection rate α. We conducted some numerical simulations to support our analytical findings.

Keywords: Tuberculosis; Basic reproduction number; Backward bifurcation; Transcritical bifurcations; Hopf-bifurcation (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437118300141
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:497:y:2018:i:c:p:52-71

DOI: 10.1016/j.physa.2018.01.014

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().