A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections

Rajivganthi Chinnathambi, Fathalla A. Rihan, Hebatallah J. Alsakaji

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we propose a fractional-order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation analysis. A discrete time delay is introduced in the model to justify the time taken for diagnosis of the disease. Existence and positivity of the solutions are investigated. Some interesting sufficient conditions that ensure the local asymptotic stability of infection-free and endemic steady states are studied. The fractional-order TB model undergoes Hopf bifurcation with respect to time delay and disease transmission rate. The presence of fractional order and time delay in the model improves the model behaviors and develops the stability results. A numerical example is provided to support our theoretical results.

Original languageEnglish
Pages (from-to)8011-8025
Number of pages15
JournalMathematical Methods in the Applied Sciences
Volume44
Issue number10
DOIs
Publication statusPublished - Jul 15 2021

Keywords

  • bifurcation
  • fractional order
  • stability
  • time delay
  • tuberculosis

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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