Optimizing Cross-Regional Lockdown Policies for Epidemics: Balancing Economic and Public Health Costs

The cross-regional spread of epidemics, such as COVID-19, poses significant challenges due to the spillover of false-negative individuals resulting from incubation periods, detection errors, and individual irrationality. This study develops a stylized model to address the trade-offs faced by the planner in designing optimal lockdown policies: curbing the cross-regional spread of epidemics while balancing economic costs and ensuring long-term sustainability. The model integrates a queuing network to calculate the influx of false-negative cases, which more accurately reflects real-world scenarios and captures the complexity of regional interactions during an outbreak. Subsequently, a SIR network is used to estimate the spread of infections. Unlike similar studies, our approach focuses specifically on the cross-regional dynamics of epidemic spread and the formulation of optimal lockdown policies that consider both public health and economic impacts. By optimizing the lockdown threshold, the model aims to minimize the total costs associated with lockdown implementation and infection spread. Our theoretical and numerical results underscore the crucial role of timely nucleic acid testing in reducing infection rates and highlight the delicate balance between public health benefits and economic sustainability. These findings provide valuable insights for developing sustainable epidemic management strategies.