In general, different countries and communities respond to epidemics in accordance with their own control plans and protocols. However, owing to global human migration and mobility, strategic planning for epidemic control measures through the collaboration of relevant public health administrations is gaining importance for mitigating and containing large-scale epidemics. Here, we present a framework to evaluate the effectiveness of random (non-strategic) and targeted (strategic) epidemic interventions for spatially separated patches in metapopulation models. For a random intervention, we analytically derive the critical fraction of patches that receive epidemic interventions, above which epidemics are successfully contained. The analysis shows that the heterogeneity of patch connectivity makes it difficult to contain epidemics under the random intervention. We demonstrate that, particularly in such heterogeneously connected networks, targeted interventions are considerably effective compared to the random intervention. Our framework is useful for identifying the target areas where epidemic control measures should be focused. M odern transportation and traffic networks have enabled people to travel more frequently and globally than before, and therefore, epidemic outbreaks in local regions can potentially threaten international public health. The diversity and complexity of human mobility patterns complicate the planning of effective control measures against global epidemics at a local level. Therefore, epidemic control planning through international and inter-community cooperation is increasingly gaining importance to mitigate the threat of public health emergency caused by global epidemics [1] [2] [3] . The challenges to improve the detection and containment of epidemics with international importance have been addressed in international surveillance and response programs 4 , such as Global Outbreak Alert and Response Network (GOARN) 5 supported by the World Health Organization (WHO). The collaboration networks of public health administrations and research institutes are expected to contribute to the planning of strategies and policies for better epidemic control measures. An assessment of the impact of potential control strategies is a critical issue for policymakers to implement them. A metapopulation model is a useful mathematical framework to understand the dynamics of epidemic spreading in spatially separated patches, corresponding to countries, cities, or local communities, which are connected by pathways for human migration and population mobility [6] [7] [8] [9] . Data analyses revealed the heterogeneous structures of transportation networks such as airline networks [10] [11] [12] , railway networks 13, 14 , and commuting networks 15, 16 , and therefore, metapopulation models with complex patch connectivity have been intensively studied [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] . A major concern in these studies has been the global epidemic threshold, which determines if a global epidemic occurs or not when a small number of infected individuals invade a local patch 16, 19, 20, [23] [24] [25] . The metapopulation framework has also been widely employed to investigate the efficacy of containment measures such as travel restrictions 19, 21, 28, 29 , vaccinations 17 , and therapeutic use of antiviral drugs . Colizza et al. 21 demonstrated that the redistribution of the stockpiles of antiviral drugs between prepared and unprepared countries is effective under limited antiviral supplies. However, such a cooperative strategy for controlling the infection of subpopulations in local patches has yet to be fully examined. Here, we present a metapopulation framework to evaluate the effectiveness of strategic interventions for epidemic control as compared to a non-strategic intervention. We consider a public health intervention that significantly reduces the infection risk of a subpopulation in a local patch through various countermeasures, e.g., the surveillance of cases and health indicators, delivery of vaccines, distribution of antiviral drugs, and promotion of hand hygiene. Public health interventions are provided to a fraction p of the patches, which we refer to as the low-risk patches 30 . We assume that the infection rate in the low-risk patches is lower than that in the other patches
The authors in REF proposed a framework to evaluate the effectiveness of random and targeted epidemic interventions for spatially separated patches in meta-population models.
Random and Targeted Interventions for Epidemic Control in Metapopulation Models
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