标题： 基于均场博弈的网络上流行病传播方法 显示英文标题

标题： Mean-field game approach to epidemic propagation on networks

摘要： 我们研究了在平均场博弈背景下网络上流行病传播的SIR模型。 在真实的流行病中，个体根据流行病的水平以及它可能对未来产生的影响来调整自己的行为。 这些个体行为反过来会影响流行病的动态变化。 平均场博弈是一种可以捕捉这些反馈效应的框架。 我们推导了以个体接触率为基准的流行病数量的动力学方程，并通过平均场近似得到了与某种成本函数最小化相关的纳什均衡。 我们首先考虑同质网络，其中所有个体具有相同数量的邻居，并讨论当该数量变化时个体行为如何改变。 然后我们研究了一个基于社会接触网络真实数据的现实异质网络的情况。 我们的结果有助于评估这种方法在现实世界实施中用于流行病缓解的潜力。 显示英文摘要

摘要： We investigate an SIR model of epidemic propagation on networks in the context of mean-field games. In a real epidemic, individuals adjust their behavior depending on the epidemic level and the impact it might have on them in the future. These individual behaviors in turn affect the epidemic dynamics. Mean-field games are a framework in which these retroaction effects can be captured. We derive dynamical equations for the epidemic quantities in terms of individual contact rates, and via mean-field approximations we obtain the Nash equilibrium associated with the minimization of a certain cost function. We first consider homogeneous networks, where all individuals have the same number of neighbors, and discuss how the individual behaviors are modified when that number is varied. We then investigate the case of a realistic heterogeneous network based on real data from a social contact network. Our results allow to assess the potential of such an approach for epidemic mitigation in real-world implementations.