Abstract This paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number R0 $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R0≤1 $\mathcal R_0 \leq 1$, while when R0>1 $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.

中文翻译：

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一类具有多个感染阶段的流行病学模型的数学研究

摘要 本文涉及对传染病传播动态的具有多个感染阶段的一类通用流行病学模型进行数学分析。我们提供了该模型的理论研究。我们推导出基本繁殖数 R0 $\mathcal R_0$，它决定了感染的灭绝和持续性。我们证明，当 R0≤1 $\mathcal R_0 \leq 1$ 时，无病平衡是全局渐近稳定的，而当 R0>1 $\mathcal R_0 \gt 1$ 时，无病平衡是不稳定的，存在一个全球渐近稳定的独特地方性平衡点。结核病 (TB) 案例研究被认为在数值上支持分析结果。