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.

本文讨论了一个简单的结核病的确定性流行病模型。研究了有效接触率，治疗率和不完全治疗与有效治疗的关系。我们还分析了结核感染的渐近行为，传播和可能的根除。观察到疾病传播动力学的特征在于基本繁殖率\（\ Re _ {0} \） ; 如果\（\ Re _ {0} <1 \），则只有无病平衡，局部和全局渐近稳定。此外，对于\（\ Re _ {0}> 1 \），存在一个独特的正地方性平衡，该平衡是全局渐近稳定的。平衡的全局稳定性通过Lyapunov函数显示。还得到的是，对结核病的不完全治疗导致疾病感染的增加，而有效的治疗导致结核病的减少。最后，对于估计的参数，执行一些数值模拟以验证分析结果。这些数值结果表明有效接触率λ的降低和治疗率γ的提高在结核病感染控制中起着重要作用。