流行病与行为

摘要：

我们研究流行病期间的均衡距离。保持距离可以降低个人感染的可能性，但这是有代价的。它创造了一个单峰流行病，使曲线变短，并减少了流行病的规模。我们更仔细地研究了距离对疫情开始、高峰和最终规模的影响。首先，我们定义了一个行为基本再生数，并证明了它是凹的传输率。因此，只有当传播率处于中间区域时，感染才会传播。二是疫情高峰在传播率上具有非单调性。传输速率的降低可导致峰值的增加。另一方面，距离成本的降低总是会使曲线变平。第三，感染率的增加以及保持距离的成本的增加都增加了流行病的规模。我们的研究结果对干预措施的建模具有重要意义。对感染率施加限制与对距离成本施加假设对流行病的轨迹产生了质的不同影响。因此，影响互动而不是传播率的干预措施应该被建模为距离成本的变化。

英文摘要：

We study equilibrium distancing during epidemics. Distancing reduces the individual's probability of getting infected but comes at a cost. It creates a single-peaked epidemic, flattens the curve and decreases the size of the epidemic. We examine more closely the effects of distancing on the outset, the peak and the final size of the epidemic. First, we define a behavioral basic reproduction number and show that it is concave in the transmission rate. The infection, therefore, spreads only if the transmission rate is in the intermediate region. Second, the peak of the epidemic is non-monotonic in the transmission rate. A reduction in the transmission rate can lead to an increase of the peak. On the other hand, a decrease in the cost of distancing always flattens the curve. Third, both an increase in the infection rate as well as an increase in the cost of distancing increase the size of the epidemic. Our results have important implications on the modeling of interventions. Imposing restrictions on the infection rate has qualitatively different effects on the trajectory of the epidemics than imposing assumptions on the cost of distancing. The interventions that affect interactions rather than the transmission rate should, therefore, be modeled as changes in the cost of distancing.

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