Elsevier

Journal of Theoretical Biology

Volume 454, 7 October 2018, Pages 320-329
Journal of Theoretical Biology

Metapopulation model using commuting flow for national spread of the 2009 H1N1 influenza virus in the Republic of Korea

https://doi.org/10.1016/j.jtbi.2018.06.016Get rights and content

Highlights

  • Spatial-temporal pattern of the nationwide spread of 2009 H1N1 influenza in Korea is studied.

  • Metapopulation model linked by commuting flow is used.

  • Local reproductive number and peak time at province level are investigated.

  • Interventions at the source of infection is more effective than those at the commuting-hub.

Abstract

We study the spatial-temporal pattern of the spread of the 2009 H1N1 influenza virus using a metapopulation model linked by commuting flow based on the reported influenza cases during the early stages of the epidemic in the Republic of Korea. The spatial heterogeneities, such as the local reproductive number and peak time, are investigated at province level. Furthermore, we discuss the effect of early intervention strategies, isolation and commuting restrictions, on the reduction of incidence at each province level. A major finding of this study is that early intervention at the source area of infection is more effective than interventions at the commuting-hub areas if the cost is limited.

Introduction

Beginning in April 2009, the H1N1 influenza virus rapidly spread worldwide after several cases of severe respiratory illness were confirmed as the H1N1 influenza virus in Mexico. The World Health Organization (WHO) declared a global outbreak of the H1N1 flu virus and raised the influenza pandemic alert level to Phase 5 on April 30, 2009 (World Health Organization, 2009). The Korea Centers for Disease Control & Prevention (KCDC) reported that the first confirmed case of the H1N1 flu occurred at Gwacheon on April 27, 2009 and escalated the national public health crisis phase from “Attention” to “Caution” (Lee et al., 2013a). During the early period of a novel influenza pandemic, when pharmaceutical interventions were lacking, non-pharmaceutical control measures for public health were the most critical strategies for impeding the spread of influenza and delaying the epidemic. Furthermore, spatial-temporal disease transmission dynamics during the early period represented the most critical issue in terms of influenza epidemic prevention.

Mathematical modeling has been a crucial tool for understand the transmission dynamics of the influenza pandemic, especially the spatial-temporal spread of influenza in the early stage of the outbreak. Mathematical models have also provided science-based health policy tools for predicting effective intervention strategies for migrating future pandemics. Baroyan and Rvachev first introduced a deterministic model governed by partial differential equations for a society containing a transportation network (Baroyan and Rvachev, 1967). Baroyan et al. developed a deterministic model with transportation network in the Soviet Union (Baroyan et al., 1971), which was a combination of the Kermack–McKendrick SEIR model for inner-city disease dynamics and a linear transport operator for inter-city traveling flows. Sattenspiel and Dietz introduced an infectious disease transmission model governed by ordinary differential equations that incorporated the mobility process between subpopulations to keep track of individuals who resides in patch i and travels in patch j at a given time (Sattenspiel and Dietz, 1995). They proceeded to describe a 1984 measles epidemic on the Caribbean island of Dominica, and showed that individual movement could be expressed in terms of the between-city contact rates (Sattenspiel and Herring, 2003). Such spatial-temporal models involving movement of individuals between discrete spatial patches have been further analyzed for the basic reproductive number by Arino and coauthor (Arino, Davis, Hartley, Jordan, Miller, van Den Driessche, 2005, Arino, Van den Driessche, 2003). Hyman and Laforce introduced the SIR model of influenza using nonrandom population mixing among cities according to the migration rate, which was based on airline flight data for the 33 largest US cities from 1996 to 2001 (Hyman and Laforce, 2003). They used a symmetric matrix to maintain a constant population size of each city. Wang and Zhao considered a theoretical approach to investigate the threshold of disease persistence according to population dispersal among patches (Wang, Mulone, 2003, Wang, Zhao, 2004). They demonstrated that disease spread can be controlled by the dispersal rates of the subpopulation. Colizza et al. developed stochastic models of the global influenza spread using airline data to investigate the diffusion pattern of a disease (Colizza et al., 2006) and the effectiveness of travel restrictions and antiviral drug distribution worldwide (Colizza et al., 2007). Viboud et al. introduced a spatially extended stochastic model that included influenza related mortality and workflow data in the United States (Viboud et al., 2006). They showed that the spread of influenza correlated more strongly with migration than the Euclidian distance. Ferguson et al. developed a pandemic spread stochastic model in Southeast Asia and constructed a spatially explicit simulation of the 85 million people residing in Thailand and within 100 km wide zone of the contiguous neighboring countries (Ferguson et al., 2005). Recently, Herrera et al. constructed a deterministic model with discrete spatial patches to investigate the role of transportation flow on the 2009 H1N1 pandemic influenza in Maxico (Herrera-Valdez et al., 2011). They used the relative contribution of each patch to the total daily flux through the main patch, rather than the exact daily number of individuals traveling from one patch to another patch. Chowell and colleagues developed an influenza model in Mexico using data from the winter of 2013–2014 (Dávila et al., 2013) and a stochastic model of spatial-temporal transmission of influenza in China and Peru (Chowell, Viboud, Munayco, Gómez, Simonsen, Miller, Tamerius, Fiestas, Halsey, Laguna-Torres, 2011, Xiao, Lin, Chowell, Huang, Gao, Chen, Wang, Zhou, He, Liu, et al., 2014).

While many metapopulation models have been employed to explore the 2009 H1N1 influenza pandemic, here we focus on the impact of commuting network structures in the Republic of Korea on the spread of the virus into the local community and its control measures. We use the spatial-temporal transmission model developed by Lee and Jung (2015) during the 2009 H1N1 influenza pandemic. In this previous study, the spatial-temporal spreading pattern for the 2009 H1N1 influenza was investigated through the model driven by the data including commuting movement and flu-patients within only the Seoul Metropolitan Area (SMA) in the Republic of Korea. In this work, the spatial-temporal model including commuting is expanded to the entire country. The whole country is divided into seven integrated regions, and the laboratory-confirmed cases and commuting data at the a district-level are aggregated into each region to investigate the spatial-temporal patterns of the 2009 H1N1 flu spread in a nationwide scale. The results of simulated spatial-temporal transmission of influenza are described using a Geographic Information System (GIS). As this study focuses on the early spread of influenza, non-pharmaceutical control measures, i.e., the isolation control and the commuting restrictions, are considered as interventions for delaying the local outbreak. Furthermore, we investigate the effect of early interventions at the source areas of infection and/or the commuting-hub areas at each of the seven integrated regions.

The remainder of this paper is structured as follows. In Section 2, the epidemiological and geographical data, as well as the commuting networks for influenza modeling are introduced. The spatial-temporal model for the nation-wide influenza epidemic is also presented in this section. In Section 3, the simulation results for transmission dynamics of the 2009 H1N1 influenza virus in the entire country are discussed. The effects of the non-pharmaceutical interventions based on the centrality analysis are discussed in this section. The conclusions are presented in Section 4.

Section snippets

Epidemiological data

The H1N1 case data in the Republic of Korea consist of two different sets: daily laboratory-confirmed H1N1 influenza cases from April 27 to September 15, 2009, and cases that were prescribed the antiviral drugs in the later stage of the epidemic (Lee et al., 2013a). Due to this inconsistency of data and considering the main goal of this study, we used the daily laboratory-confirmed cases in the early stage of the epidemic for developing the spatial-temporal model of the 2009 H1N1 influenza

Spatial-temporal pattern of the nationwide spread

The spatial-temporal pattern of the nationwide spread of the 2009 H1N1 influenza virus was explored in every week after the onset of the outbreak using GIS, with colors from green to red indicating cumulative incidence (Fig. 5). We found that the local outbreak in each integrated region widely spreads not only within the district but also the adjacent districts through the regular commuting flow. Although the pattern of spatial-temporal spread is too complex to fully understand, our results

Conclusion

In this work, the spatial-temporal transmission model of the 2009 H1N1 influenza virus in the SMA (Lee and Jung, 2015) was extended to the nationwide model of the Republic of Korea, in order to find the localized contribution factors to the 2009 H1N1 influenza virus and measure the impact of early intervention strategies. For this purpose, a total of 160 districts (municipal-level) were integrated into seven regions (province-level) based on commuting data and geographic proximity. The daily

Acknowledgments

This paper was supported by Konkuk University in 2017.

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