Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, C1428EGA, Buenos Aires, Argentina.
Departamento de Física, Instituto de Física de Mar del Plata (IFIMAR) CONICET, UNMDP, Universidad Nacional de Mar del Plata, Funes 3350, 7600, Mar del Plata, Argentina.
Sci Rep. 2022 Jul 22;12(1):12583. doi: 10.1038/s41598-022-16619-z.
Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short period of time. Here we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model with a limitation on the total duration of the quarantine. The control is done by means of the reproduction number [Formula: see text], i.e., the number of secondary infections produced by a primary infection, which can be arbitrarily varied in time over a quarantine period T to account for external interventions. We also assume that the most strict quarantine (lower bound of [Formula: see text]) cannot last for a period longer than a value [Formula: see text]. The aim is to minimize the cumulative number of ever-infected individuals (recovered) and the socioeconomic cost of interventions in the long term, by finding the optimal way to vary [Formula: see text]. We show that the optimal solution is a single bang-bang, i.e., the strict quarantine is turned on only once, and is turned off after the maximum allowed time [Formula: see text]. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, [Formula: see text] and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.
社交距离、隔离和全面封锁是非药物干预措施，政策制定者已利用这些措施来减缓 COVID-19 病毒的传播。然而，这些措施可能会对社会的社会和经济成本造成损害，而且它们只能维持很短的时间。在这里，我们通过研究具有隔离总持续时间限制的易感-感染-恢复模型的最优控制条件，来研究将传染病的影响降至最低的最佳策略。通过繁殖数 [Formula: see text]（即一次原发性感染产生的二次感染数）进行控制，这可以在隔离期 T 内任意变化，以考虑外部干预。我们还假设最严格的隔离（[Formula: see text]的下限）不能持续超过 [Formula: see text]的时间。我们的目标是通过找到改变 [Formula: see text]的最佳方式，来最小化长期内累计受感染个体（恢复者）的数量和干预的社会经济成本。我们表明，最优解是一个单一的 bang-bang，即严格的隔离只开启一次，并且在最大允许时间 [Formula: see text]后关闭。此外，我们计算了开始和结束严格隔离的最佳时间，这取决于 T、[Formula: see text]和初始条件。我们提供了这些结果的严格证明，并通过数值计算进行了验证。
