论文标题
大流行期间社会疏远的经济成本：SVIR模型中的最佳控制方法
The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model
论文作者
论文摘要
我们为传染病的最佳动力学控制设计了一个理论模型，该模型的扩散是由SVIR隔室模型描述的。通过实施社会规则来减少疾病的传播，这通常意味着大量的经济和社会成本来实现控制。我们通过引入功能取决于三个任期的功能来对这种权衡进行建模：社会成本功能，受感染人群的医疗保健系统支持的成本以及疫苗接种运动的成本。使用Pontryagin的最大原则，我们为存在最佳策略的存在提供了条件，我们在社会成本函数的三个实例中明确表征了这一条件，分别是线性，二次和指数模型。最后，我们通过使用最近COVID的意大利数据-19模型校准的大流行，在最佳控制系统的数值解上提供了一组结果。
We devise a theoretical model for the optimal dynamical control of an infectious disease whose diffusion is described by the SVIR compartmental model. The control is realized through implementing social rules to reduce the disease's spread, which often implies substantial economic and social costs. We model this trade-off by introducing a functional depending on three terms: a social cost function, the cost supported by the healthcare system for the infected population, and the cost of the vaccination campaign. Using the Pontryagin's Maximum Principle, we give conditions for the existence of the optimal policy, which we characterize explicitly in three instances of the social cost function, the linear, quadratic, and exponential models, respectively. Finally, we present a set of results on the numerical solution of the optimally controlled system by using Italian data from the recent Covid--19 pandemic for the model calibration.
