Final size index-driven strategies for cost-effective epidemic management in metapopulation

Designing effective control strategies for managing epidemics in metapopulations, where human mobility plays a critical role, is essential for public health policies. In this paper, we propose a novel methodology for efficiently distributing control resources by considering both the epidemiological response of each region and the cost of implementing a control strategy to reduce contact rates within a given patch. Specifically, using the SEIR (Susceptible-Exposed-Infectious-Recovered) model to describe the epidemic process in each patch of the metapopulation, we derive a mathematical expression for the epidemic's final size in each patch, which measures the total number of individuals that become infected by the end of the epidemic. By solving this expression with an interactive approach, we guarantee computational efficiency even in large and highly connected metapopulations. Based on the final size of each patch, we propose an index to guide the control strategy efficiently. We compare this approach with other intuitive strategies, such as allocating all control resources to the most affected patch or distributing resources homogeneously. Our findings suggest that allocating control resources proportionally to the final size index best allocates resource returns across multiple zones. This strategy results in similar epidemic trajectories across regions, prevents resource concentration in a few areas, maintains lower local peaks, and ensures a more balanced epidemic impact across the metapopulation.