The optimal spatially-dependent control measures to effectively and economically eliminate emerging infectious diseases

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.Author summary: In the early stage of the outbreak of an emerging infectious disease, non-pharmaceutical interventions (NPIs) are the most effective way to control the spread of the disease given unavailability of effective medicines or vaccines. However, the implementation of NPIs may have a certain negative impact on the society and economy. There are many challenges to designing an effective and economical control regime on the basis of spatial, populate and economical heterogeneity. We developed a modelling framework to couple transmission dynamics, all possible control measures and the spatial mobility, aiming at controlling the outbreak spreading across regions and reducing the economic losses caused by control measures. We applied this framework to identify the optimal control strategy for the COVID-19 outbreak in Xi’an City, China, between December 2021 and January 2022. We analyzed the key factors related to the outbreak size and control cost, and the results showed that the outbreak size and control cost were significantly correlated with the transmissibility of the virus and the demographic and economic conditions of the epidemic area. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity.