论文标题
网络行为流动模型的平均场分析
A mean-field analysis of a network behavioural-epidemic model
论文作者
论文摘要
流行病的传播和人口的集体行为反应被深深交织在一起，影响了彼此的演变。这种共同进化通常在数学模型中被忽略，从而限制了其现实世界的适用性。为了解决这一差距，我们提出和分析了一种行为流动模型，其中易感感染感染的流行病模型以及有关使用自我保护措施使用的进化游戏理论决策机制。通过平均场方法，我们表征了系统的渐近行为，从而得出了全球收敛到无疾病平衡的条件，并表征了系统的地方均衡及其（局部）稳定性。有趣的是，对于一定范围的模型参数，我们证明了全局收敛到限制周期，其特征是周期性的流行病暴发。
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural-epidemic model, in which a susceptible-infected-susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks.
