Stability analysis of a dynamical model of tuberculosis with incomplete treatment

Ihsan Ullah, Saeed Ahmad, Qasem Al-Mdallal, Zareen A. Khan, Hasib Khan, Aziz Khan

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio ℜ ; if ℜ < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for ℜ > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

Original languageEnglish
Article number499
JournalAdvances in Difference Equations
Issue number1
Publication statusPublished - Dec 1 2020


  • Basic reproduction ratio
  • Deterministic model
  • Global stability
  • Local stability
  • Lyapunov function
  • Tuberculosis

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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