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Abstract：
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. the network 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 also 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. This means that our minimal model is not able to reproduce consequent waves of an epidemic, and more complex disease or behavioural dynamics are required to reproduce epidemic waves.
摘要：
疾病传播与个人风险感知之间的相互作用对于模拟传染病的传播至关重要。我们提出了一个常微分方程（ODE）的平面系统，以描述个人接触网络中的传播现象和平均链接密度的共同演化。与标准流行病模型相反，我们假设接触网络根据当前人群中疾病的患病率而变化，即网络适应当前的流行状态。我们假设使用两种功能响应来描述个人风险感知：一种用于链接中断，一种用于链接创建。重点是将该模型应用于流行病，但我们也强调了其他可能的应用领域。我们推导了基本复制数的显式形式，并保证至少存在一个地方性均衡，所有可能的功能性反应。此外，我们表明，对于所有功能响应，极限循环不存在。这意味着我们的最小模型无法重现随之而来的流行病浪潮，需要更复杂的疾病或行为动力学来重现流行病。
