论文标题
COVID-19的接触率流行控制：平衡视图
Contact rate epidemic control of COVID-19: an equilibrium view
论文作者
论文摘要
我们考虑通过标准的SIR隔室模型来控制Covid-19的大流行。这种控制是由个人决定限制其社交互动的决策所引起的：当流行病正在进行时，一个人可以降低他/她的接触率，以避免被感染，但这种努力是以社会成本的。如果每个人都降低了他/她的接触率，那么流行病就会更快地消失，但是努力的成本可能很高。形成了种群水平的平均纳什平衡，导致病毒的有效传播速率较低。从理论上讲，我们证明存在平衡并以数值计算。但是，这种均衡选择了与社会最佳最佳（所有个人完全尊重的集中决策）相比，选择了一个最佳的解决方案，这意味着无政府状态的成本严格是积极的。我们提供数值示例和灵敏度分析，以及对SEIR隔室模型的扩展，以说明COVID-19疾病的相对较长的潜在阶段。在所有情况下，考虑到个人和社会策略之间的差异都发生在流行病的高峰之前，由于个人的恐惧以及之后，当大量传播仍在进行中。
We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals' decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralized decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. We provide numerical examples and a sensitivity analysis, as well as an extension to a SEIR compartmental model to account for the relatively long latent phase of the COVID-19 disease. In all the scenarii considered, the divergence between the individual and societal strategies happens both before the peak of the epidemic, due to individuals' fears, and after, when a significant propagation is still underway.
