School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China.
Department of Mathematics and Statistics, University of Victoria, Victoria, Canada.
PLoS Comput Biol. 2024 Oct 7;20(10):e1012498. doi: 10.1371/journal.pcbi.1012498. eCollection 2024 Oct.
Non-pharmaceutical interventions (NPIs) are effective in mitigating infections during the early stages of an infectious disease outbreak. However, these measures incur significant economic and livelihood costs. To address this, we developed an optimal control framework aimed at identifying strategies that minimize such costs while ensuring full control of a cross-regional outbreak of emerging infectious diseases. Our approach uses a spatial SEIR model with interventions for the epidemic process, and incorporates population flow in a gravity model dependent on gross domestic product (GDP) and geographical distance. We applied this framework to identify an optimal control strategy for the COVID-19 outbreak caused by the Delta variant in Xi'an City, Shaanxi, China, between December 2021 and January 2022. The model was parameterized by fitting it to daily case data from each district of Xi'an City. Our findings indicate that an increase in the basic reproduction number, the latent period or the infectious period leads to a prolonged outbreak and a larger final size. This indicates that diseases with greater transmissibility are more challenging and costly to control, and so it is important for governments to quickly identify cases and implement control strategies. Indeed, the optimal control strategy we identified suggests that more costly control measures should be implemented as soon as they are deemed necessary. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. More populated and economically developed regions require a robust regular surveillance mechanism to ensure timely detection and control of imported infections. Regions with higher GDP tend to experience larger-scale epidemics and, consequently, require higher control costs. Notably, our proposed optimal strategy significantly reduced costs compared to the actual expenditures for the Xi'an outbreak.
非药物干预（NPIs）在传染病爆发的早期阶段对于减轻感染非常有效。然而，这些措施会带来巨大的经济和生计成本。为了解决这个问题，我们开发了一个最优控制框架，旨在确定在确保对新发传染病的跨区域爆发进行全面控制的同时，将这些成本最小化的策略。我们的方法使用了带有干预措施的空间 SEIR 模型来描述传染病的发生过程，并将人口流动纳入了一个依赖国内生产总值（GDP）和地理距离的引力模型中。我们将这个框架应用于确定中国陕西省西安市 2021 年 12 月至 2022 年 1 月期间由德尔塔变异株引起的 COVID-19 爆发的最优控制策略。该模型通过拟合西安市每个区的每日病例数据进行参数化。我们的研究结果表明，基本再生数、潜伏期或传染期的增加会导致疫情持续时间延长和最终规模增大。这表明传染性更强的疾病更难控制，成本也更高，因此政府必须迅速发现病例并实施控制策略。事实上，我们确定的最优控制策略表明，一旦认为有必要，就应该实施成本更高的控制措施。我们的研究结果表明，最优控制策略具有空间、经济和人口异质性。人口更多和经济更发达的地区需要一个稳健的常规监测机制，以确保及时发现和控制输入性感染。GDP 较高的地区往往会出现更大规模的疫情，因此需要更高的控制成本。值得注意的是，与西安市疫情的实际支出相比，我们提出的最优策略显著降低了成本。
