论文标题
重新访问Covid-19时代的SIR：明确的解决方案和控制问题
Revisiting SIR in the age of COVID-19: Explicit Solutions and Control Problems
论文作者
论文摘要
提出和研究了保护爵士（SIR-NC）模型的非个人人口（SIR-NC）模型，并研究了感染在社区中的传播。与标准的SIR模型不同，SIR-NC不假定人口保护。尽管与标准SIR相似，但Sir-NC允许我们对死亡率进行建模，并提供了对模型参数的不同，更现实的解释。提供了该SIR-NC模型与标准，人口保护的SIR模型的数值比较。提出和分析包括进口感染，相互作用的社区以及包括出生和死亡的模型的扩展。还提供了几个数值示例，以说明这些模型。提出了SIR-NC流行模型的两个控制问题。首先，我们考虑连续的时间模型预测控制，其中成本函数变量对应于锁定水平，测试水平和隔离水平以及感染的数量。我们还包括在锁定水平之间移动的切换成本。然后，与数值插图一起介绍了更适合计算的离散时间版本。然后，我们考虑一个多目标和多社区控制，我们可以在不同社区上定义多个成本功能，并获得最低成本控制，以使价值函数保持在规定的阈值以下的这些控制目标相对应。
The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the standard SIR, SIR-NC admits a closed form solution while allowing us to model mortality, and also provides different, and arguably a more realistic, interpretation of the model parameters. Numerical comparisons of this SIR-NC model with the standard, population conserving, SIR model are provided. Extensions to include imported infections, interacting communities, and models that include births and deaths are presented and analyzed. Several numerical examples are also presented to illustrate these models. Two control problems for the SIR-NC epidemic model are presented. First we consider the continuous time model predictive control in which the cost function variables correspond to the levels of lockdown, the level of testing and quarantine, and the number of infections. We also include a switching cost for moving between lockdown levels. A discrete time version that is more amenable to computation is then presented along with numerical illustrations. We then consider a multi-objective and multi-community control where we can define multiple cost functions on the different communities and obtain the minimum cost control to keep the value function corresponding to these control objectives below a prescribed threshold.
