论文标题
几何奇异扰动理论分析具有自发人类行为变化的流行病模型
Geometric Singular Perturbation Theory Analysis of an Epidemic Model with Spontaneous Human Behavioral Change
论文作者
论文摘要
我们考虑了一个由于皮耶罗·波莱蒂（Piero Poletti）和合作者而引起的模型，该模型将自发的人类行为变化添加到标准的Sir流行性模型中。 Poletti模型以最简单的形式添加了一个由进化游戏理论动机的微分方程，并将其添加到SIR模型中。新方程式描述了使用正常行为代表人口比例的变量$ x $的演变。剩余的分数$ 1-x $使用改变的行为，例如呆在家里，社交隔离，面具戴戴等。正常行为在感染数量较低时会带来更高的回报。当数字较高时，改变的行为可提供更高的回报。我们表明，几何奇异扰动理论的入门效果可用于分析模型的限制，在该模型上，行为在时间尺度上的变化比流行病的时间更快。特别是，在不同的行为的回报较高的情况下，行为不会立即改变；当前行为是粘的。延迟直到行为变化在入门级函数中预测的延迟。
We consider a model due to Piero Poletti and collaborators that adds spontaneous human behavioral change to the standard SIR epidemic model. In its simplest form, the Poletti model adds one differential equation, motivated by evolutionary game theory, to the SIR model. The new equation describes the evolution of a variable $x$ that represents the fraction of the population using normal behavior. The remaining fraction $1-x$ uses altered behavior such as staying home, social isolation, mask wearing, etc. Normal behavior offers a higher payoff when the number of infectives is low; altered behavior offers a higher payoff when the number is high. We show that the entry-exit function of geometric singular perturbation theory can be used to analyze the model in the limit in which behavior changes on a much faster time scale than that of the epidemic. In particular, behavior does not change as soon as a different behavior has a higher payoff; current behavior is sticky. The delay until behavior changes in predicted by the entry-exit function.
