Pandemics can bring a range of devastating consequences to public health and the world economy. Identifying the most effective control strategies has been the imperative task all around the world. Various public health control strategies have been proposed and tested against pandemic diseases (e.g., COVID-19). We study two specific pandemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; and the SEIR model with shield immunity control. We express the pandemic control requirement in metric temporal logic (MTL) formulas. We then develop an iterative approach for synthesizing the optimal control strategies with MTL specifications. We provide simulation results in two different scenarios for robust control of the COVID-19 pandemic: one for vaccination control, and another for shield immunity control, with the model parameters estimated from data in Lombardy, Italy. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications with robustness against initial state and parameter uncertainties.

翻译：确定最有效的控制战略是全世界必须完成的任务。我们提出了各种公共卫生控制战略,并测试了防治流行病的战略(如COVID-19)。我们研究了两种具体的流行病控制模式:具有免疫控制的易感染、接触、传染、恢复(SEIR)模式;以及具有防护豁免控制的SEIR模式。我们用时间逻辑(MTL)公式表达流行病控制要求。然后,我们制定了一种迭代方法,将最佳控制战略与MTL规格结合起来。我们提供了两种不同情景的模拟结果,以严格控制COVID-19大流行病:一种是疫苗控制,另一种是防护免疫控制,根据意大利伦巴迪的数据估计了模型参数。结果显示,拟议的综合方法可以产生控制投入,使每一类别(例如感染、免疫)中个人的时间变化数量能够可靠地满足MTL规格,避免初始状态和参数的不确定性。