Universidad Rey Juan Carlos Camino del Molino 5, 28942 Fuenlabrada, Madrid, Spain.
Comput Methods Programs Biomed. 2021 Nov;211:106411. doi: 10.1016/j.cmpb.2021.106411. Epub 2021 Sep 21.
Assuming the availability of a limited amount of effective COVID-19 rapid tests, the effects of various vaccination strategies on SARS-CoV-2 virus transmission are compared for different vaccination scenarios characterized by distinct limitations associated with vaccine supply and administration.
The vaccination strategies are defined by solving optimal control problems of a compartmental epidemic model in which the daily vaccination rate and the daily testing rate for the identification and isolation of asymptomatic subjects are the control variables. Different kinds of algebraic constraints are considered, representing different vaccination scenarios in which the total amount of vaccines available during the time period under consideration is limited or the number of daily available vaccines is limited. These optimal control problems are numerically solved by means of a direct transcription technique, which allows both equality and inequality constraints to be straightforwardly included in the formulation of the optimal control problems.
Several numerical experiments are conducted, in which the objective functional to be minimized is a combination of the number of symptomatic and asymptomatic infectious subjects with the cost of vaccination of susceptible subjects and testing of asymptomatic infectious subjects. The results confirm the hypothesis that the implementation of early control measures significantly reduces the number of symptomatic infected subjects, which is a key aspect for the resilience of the healthcare system. The sensitivity analysis of the solutions to the weighting parameters of the objective functional reveals that it is possible to obtain a vaccination strategy that allows vaccination supplies to be saved while keeping the same number of symptomatic infected subjects. Furthermore, it indicates that if the vaccination plan is not supported by a sufficient rate of testing, the number of symptomatic infected subjects could increase. Finally, the sensitivity analysis shows that a significant reduction in the efficacy of the vaccines could also lead to a relevant increase in the number of symptomatic infected subjects.
The numerical experiments show that the proposed approach, which is based on optimal control of compartmental epidemic models, provides healthcare systems with a suitable method for scheduling vaccination plans and testing policies to control the spread of the SARS-CoV-2 virus.
假设可获得有限数量的有效 COVID-19 快速检测试剂，那么对于不同的疫苗接种方案，在疫苗供应和管理方面存在明显限制的不同接种场景下，比较各种疫苗接种策略对 SARS-CoV-2 病毒传播的影响。
通过求解一个具有不同代数约束的房室流行模型的最优控制问题来定义疫苗接种策略，该模型中每日接种率和无症状个体识别与隔离的每日检测率为控制变量。考虑了不同种类的代数约束，代表了不同的接种场景，其中在考虑时间段内可获得的疫苗总量有限或每日可获得的疫苗数量有限。这些最优控制问题通过直接转录技术进行数值求解，该技术允许直接将等式和不等式约束纳入最优控制问题的公式中。
进行了多项数值实验，其中要最小化的目标函数是无症状和有症状感染个体数量与易感个体接种疫苗和无症状感染个体检测成本的组合。结果证实了这样一个假设，即实施早期控制措施可显著减少有症状感染者的数量，这是医疗保健系统弹性的一个关键方面。对目标函数加权参数的解的敏感性分析表明，可以获得一种疫苗接种策略，在保持相同数量的有症状感染个体的同时，节省疫苗接种供应。此外，这表明如果接种计划没有足够的检测率支持，那么有症状感染者的数量可能会增加。最后，敏感性分析表明，如果疫苗的效力显著降低，也可能导致有症状感染者数量的显著增加。
数值实验表明，所提出的方法基于房室流行模型的最优控制，为医疗保健系统提供了一种合适的方法，用于安排疫苗接种计划和检测策略，以控制 SARS-CoV-2 病毒的传播。
