Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada.
Math Biosci Eng. 2012 Apr;9(2):393-411. doi: 10.3934/mbe.2012.9.393.
An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number R0 gives a sharp threshold. If R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If R0 > 1, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable.
重新研究了具有任意分布潜伏期的 SEIR 传染病模型，以研究异质性对传染病传播的影响。这种异质性可能来自年龄或行为以及疾病阶段，分别导致多组和多阶段模型。对于每个模型，使用李雅普诺夫泛函证明基本再生数 R0 给出了一个明显的阈值。如果 R0 ≤ 1，则无病平衡点全局渐近稳定，疾病从所有组或阶段中消失。如果 R0 > 1，则疾病在所有组或阶段中持续存在，地方病平衡点全局渐近稳定。
