Abstract
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 Re _{0}; if Re _{0}<1, there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for Re _{0}>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.
Highlights
Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis, which most frequently affects the lungs (pulmonary TB)
1 Introduction Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis, which most frequently affects the lungs
The symptoms and signs of active TB include: coughing that lasts for about two weeks, fever, chest pain, weight loss, fatigue, night sweats
Summary
Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis, which most frequently affects the lungs (pulmonary TB). Mathematical modeling has a great role in predicting the transmission dynamics and construction of control strategies for a disease. Distinct models for TB transmission dynamics have been developed [5,6,7,8,9] either to provide strategies for TB spread/control or to evaluate its rampaged effect. Zhang and Feng [11] proposed a TB model to study its spread in a host population incorporating incomplete treatment and isolation.
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