Mathematical Analysis of the Transmission Dynamics of Tuberculosis

• 作者: Israt Sultana Jannatun Nayeem
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: TUBERCULOSIS MODEL SIR MODEL EQUILIBRIA Stability Castillo-Chavez Theorem DISEASE Dynamics DISEASE ENDEMIC Equilibrium
• 年，卷（期）: 2019,（3）
• 页码范围: 158-173
• 页数: 16页
• 分类号: O1

摘要

We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.