纳什流行病
Nash epidemics
AI总结：
本文研究流行病中理性社交距离的纳什均衡，利用新解析解揭示行为与感染数的关系、标度规律及特征成本，为个人和政策制定者提供直观理解。
摘要：
面对危险的流行病，人类会自发地保持社交距离，以在社会经济成本下降低感染风险。分室流行病模型已被扩展以纳入这种内生决策：个体选择自己的行为以优化效用函数，并自洽地形成群体行为。本文研究由此产生的纳什均衡的性质，在这种均衡中，群体中没有任何成员能够通过单方面采取不同行为而获得优势。我们利用一个新的解析解得到：（1）理性社交距离行为与当前感染人数之间的简单关系；（2）关于感染峰值和总病例数如何取决于感染疾病成本的新标度结果；（3）划分强行为响应和弱行为响应区间的特征感染成本，该成本仅取决于疾病的基本再生数；（4）效用值的闭式表达式。我们讨论了这些解析结果如何为疾病动力学提供深刻而直观的理解，对个人和政策制定者都很有用。特别是，社交距离与感染之间的关系代表了一种启发式方法，可以传达给公众以鼓励或“引导”理性行为。
英文摘要：
Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socio-economic cost. Compartmentalised epidemic models have been extended to include this endogenous decision making: Individuals choose their behaviour to optimise a utility function, self-consistently giving rise to population behaviour. Here we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behaviour. We leverage a new analytic solution to obtain, (1) a simple relationship between rational social distancing behaviour and the current number of infections; (2) new scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; (3) characteristic infection costs that divide regimes of strong and weak behavioural response and depend only on the basic reproduction number of the disease; (4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding into the disease dynamics, useful for both individuals and policymakers. In particular the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or "bootstrap", rational behaviour.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
