TY - JOUR
T1 - Stability analysis of a dynamical model of tuberculosis with incomplete treatment
AU - Ullah, Ihsan
AU - Ahmad, Saeed
AU - Al-Mdallal, Qasem
AU - Khan, Zareen A.
AU - Khan, Hasib
AU - Khan, Aziz
N1 - Funding Information:
This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program and the second author is thankful. Acknowledgements Availability of data and materials
Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Basic reproduction ratio
KW - Deterministic model
KW - Global stability
KW - Local stability
KW - Lyapunov function
KW - Tuberculosis
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U2 - 10.1186/s13662-020-02950-0
DO - 10.1186/s13662-020-02950-0
M3 - Article
AN - SCOPUS:85091130541
SN - 1687-1839
VL - 2020
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 499
ER -