论文标题
由Preisach操作员建模的异质传输速率的SIR模型的全球稳定性
Global stability of SIR model with heterogeneous transmission rate modeled by the Preisach operator
论文作者
论文摘要
近年来，假设个体固定行为的经典流行模型已扩展到包括人口对流行病现状的自适应异质反应。但是，人们普遍认为，人类行为可以表现出历史依赖性，这是由于学习经验的结果。这种历史依赖性类似于在控制理论中经过充分研究的滞后作用。为了说明历史依赖性对流行论的重要性，我们研究了SIRS模型变体的动力学，其中个体表现出对患病动力学的懒惰切换反应。所得模型包括Preisach磁滞算子，具有以不同比例的易感性，感染和恢复种群为特征的地方性平衡状态的连续体。我们讨论了流行平衡集的稳定性，并将其与自适应反应的异质性程度相关联。我们的结果支持这样的论点：新疾病的出现期间的公共卫生反应可能会对随后的管理工作产生长期后果。这项工作的主要数学贡献是一种全球稳定性分析的方法，该方法使用了与滞后者不同分支相对应的Lyapunov函数系列。
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely accepted that human behavior can exhibit history-dependence as a consequence of learned experiences. This history-dependence is similar to hysteresis effects that have been well-studied in control theory. To illustrate the importance of history-dependence for epidemic theory, we study dynamics of a variant of the SIRS model where individuals exhibit lazy-switch responses to prevalence dynamics. The resulting model, which includes the Preisach hysteresis operator, possesses a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We discuss stability properties of the endemic equilibrium set and relate them to the degree of heterogeneity of the adaptive response. Our results support the argument that public health responses during the emergence of a new disease can have long-term consequences for subsequent management efforts. The main mathematical contribution of this work is a method of global stability analysis, which uses a family of Lyapunov functions corresponding to different branches of the hysteresis operator.
