论文标题
自适应SIS流行病的最小模型
A minimal model for adaptive SIS epidemics
论文作者
论文摘要
疾病传播与个人风险感知之间的相互作用对于建模传染病的传播至关重要。我们提出了一个普通微分方程（ODE）的平面系统，以描述传播现象的共同进化和个人接触网络中的平均链接密度。与标准流行模型相反，我们假设接触网络基于人口中疾病的当前患病率而变化，即\ \它适应流行病的当前状态。我们假设使用两个功能响应来描述个人风险感知：一种用于链接的链接，一种用于链接创造。重点是将模型应用于流行病，但我们强调了其他可能的应用领域。我们为基本的繁殖数量得出了一种明确的形式，并保证了至少存在一个特有均衡的所有可能的功能响应。此外，我们表明，对于所有功能响应，极限周期不存在。
The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of a spreading phenomenon and the average link density in the personal contact network. Contrary to standard epidemic models,we assume that the contact network changes based on the current prevalence of the disease in the population, i.e.\ it adapts to the current state of the epidemic. We assume that personal risk perception is described using two functional responses: one for link-breaking and one for link-creation. The focus is on applying the model to epidemics, but we highlight other possible fields of application. We derive an explicit form for the basic reproduction number and guarantee the existence of at least one endemic equilibrium, for all possible functional responses. Moreover, we show that for all functional responses, limit cycles do not exist.
