网络行为-流行病模型的平均场分析
A mean-field analysis of a network behavioural-epidemic model
AI总结：
本文提出并分析了一个耦合SIS流行病模型与演化博弈决策机制的行为-流行病模型，利用平均场方法给出全局收敛条件，并证明在一定参数范围内系统会全局收敛到周期性流行病暴发的极限环。
摘要：
流行病的传播与人群的集体行为反应深度交织，相互影响彼此的演化。这种协同演化在数学模型中通常被忽视，限制了模型在现实世界中的适用性。为弥补这一不足，我们提出并分析了一个行为-流行病模型，其中易感-感染-易感（susceptible-infected-susceptible）流行病模型与关于使用自我保护措施的演化博弈论决策机制相耦合。通过平均场方法，我们刻画了系统的渐近行为，推导出全局收敛到无病平衡点的条件，并刻画了系统的 endemic 平衡点及其（局部）稳定性。有趣的是，对于模型参数的某一范围，我们证明了系统全局收敛到一个极限环，其特征为周期性的流行病暴发。
英文摘要：
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.
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