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Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

Bottom Line: Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area.We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network.This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area.

View Article: PubMed Central - PubMed

Affiliation: Department of Evolutionary Studies of Biosystems (Sokendai-Hayama), The Graduate University for Advanced Studies (Sokendai), Hayama, Kanagawa, Japan; Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo, Japan.

ABSTRACT
An understanding of epidemiological dynamics is important for prevention and control of epidemic outbreaks. However, previous studies tend to focus only on specific areas, indicating that application to another area or intervention strategy requires a similar time-consuming simulation. Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area. The model is formulated on the basis of a metapopulation network in which local populations are interconnected by actual commuter flows in the Tokyo metropolitan area and the spread of infection is simulated by an individual-based model. We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network. Moreover, there is a strong relation between the population size and the time that the epidemic reaches this local population and we are able to determine the reason for this relation as well as its dependence on the commute network structure and epidemic parameters. This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area. Moreover, the clear relation of the time taken by the epidemic to reach each local population can be used as a novel measure for intervention; this enables efficient intervention strategies in each local population prior to the actual arrival.

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Schematic representation of the population size class model (PSCM).(A) Geographical distribution of the railway network; each node corresponds to a station and each line corresponds to a commuter railway of commuter trains. Every station has a home population (those who reside in the area) and a work population (those who travel to as a workplace/school in the area). There are multiple commuters using the commuter train between each pair of populations. (B) The commuter network utilized in the individual-based model (IBM) calculations. The nodes correspond to the home and work populations of each station, forming a bipartite network in which each line denotes a connection via commuter flow between home and work populations. Local populations with different population sizes are represented by different colors and sizes. (C) The commuter network utilized in the PSCM calculation. Local populations with similar population sizes are grouped into population size classes, which form the nodes, while the total commuter flows between pairs of population size classes form the lines. (D) Joint distribution of the home and work population sizes of commuters in the Tokyo metropolitan area. The number  of commuters that live in a home population of size class  and commute to a work population of size class  is plotted as a density plot. The data were obtained from the Urban Transportation Census (UTC) commute data (Ministry of Land, Infrastructure, Transport and Tourism, The 10th Urban Transportation Census Report, 2007; in Japanese).
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pone-0098518-g002: Schematic representation of the population size class model (PSCM).(A) Geographical distribution of the railway network; each node corresponds to a station and each line corresponds to a commuter railway of commuter trains. Every station has a home population (those who reside in the area) and a work population (those who travel to as a workplace/school in the area). There are multiple commuters using the commuter train between each pair of populations. (B) The commuter network utilized in the individual-based model (IBM) calculations. The nodes correspond to the home and work populations of each station, forming a bipartite network in which each line denotes a connection via commuter flow between home and work populations. Local populations with different population sizes are represented by different colors and sizes. (C) The commuter network utilized in the PSCM calculation. Local populations with similar population sizes are grouped into population size classes, which form the nodes, while the total commuter flows between pairs of population size classes form the lines. (D) Joint distribution of the home and work population sizes of commuters in the Tokyo metropolitan area. The number of commuters that live in a home population of size class and commute to a work population of size class is plotted as a density plot. The data were obtained from the Urban Transportation Census (UTC) commute data (Ministry of Land, Infrastructure, Transport and Tourism, The 10th Urban Transportation Census Report, 2007; in Japanese).

Mentions: Using these data, the daily commute movement of each individual in our individual-based model is implemented in the following way. Individuals are assumed to travel by commuter train from their residence (home population) to their workplace/school (work population), stay at their workplace/school during the day, and return from their workplace/school to their residence by the commuter train again and remain at their residence during the night (Figures 2A–B). Since the commuting data are acquired from commuter pass, this recurrent pattern only represents the commuting data of workdays. Weekend travels are generally irregular without specific patterns and we do not have the relavent data. However, since we have 2 holidays out of 7 days in a week and much less traffic flows compare to workdays, we have neglected this effect of weekends for simplicity.


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

Schematic representation of the population size class model (PSCM).(A) Geographical distribution of the railway network; each node corresponds to a station and each line corresponds to a commuter railway of commuter trains. Every station has a home population (those who reside in the area) and a work population (those who travel to as a workplace/school in the area). There are multiple commuters using the commuter train between each pair of populations. (B) The commuter network utilized in the individual-based model (IBM) calculations. The nodes correspond to the home and work populations of each station, forming a bipartite network in which each line denotes a connection via commuter flow between home and work populations. Local populations with different population sizes are represented by different colors and sizes. (C) The commuter network utilized in the PSCM calculation. Local populations with similar population sizes are grouped into population size classes, which form the nodes, while the total commuter flows between pairs of population size classes form the lines. (D) Joint distribution of the home and work population sizes of commuters in the Tokyo metropolitan area. The number  of commuters that live in a home population of size class  and commute to a work population of size class  is plotted as a density plot. The data were obtained from the Urban Transportation Census (UTC) commute data (Ministry of Land, Infrastructure, Transport and Tourism, The 10th Urban Transportation Census Report, 2007; in Japanese).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4048205&req=5

pone-0098518-g002: Schematic representation of the population size class model (PSCM).(A) Geographical distribution of the railway network; each node corresponds to a station and each line corresponds to a commuter railway of commuter trains. Every station has a home population (those who reside in the area) and a work population (those who travel to as a workplace/school in the area). There are multiple commuters using the commuter train between each pair of populations. (B) The commuter network utilized in the individual-based model (IBM) calculations. The nodes correspond to the home and work populations of each station, forming a bipartite network in which each line denotes a connection via commuter flow between home and work populations. Local populations with different population sizes are represented by different colors and sizes. (C) The commuter network utilized in the PSCM calculation. Local populations with similar population sizes are grouped into population size classes, which form the nodes, while the total commuter flows between pairs of population size classes form the lines. (D) Joint distribution of the home and work population sizes of commuters in the Tokyo metropolitan area. The number of commuters that live in a home population of size class and commute to a work population of size class is plotted as a density plot. The data were obtained from the Urban Transportation Census (UTC) commute data (Ministry of Land, Infrastructure, Transport and Tourism, The 10th Urban Transportation Census Report, 2007; in Japanese).
Mentions: Using these data, the daily commute movement of each individual in our individual-based model is implemented in the following way. Individuals are assumed to travel by commuter train from their residence (home population) to their workplace/school (work population), stay at their workplace/school during the day, and return from their workplace/school to their residence by the commuter train again and remain at their residence during the night (Figures 2A–B). Since the commuting data are acquired from commuter pass, this recurrent pattern only represents the commuting data of workdays. Weekend travels are generally irregular without specific patterns and we do not have the relavent data. However, since we have 2 holidays out of 7 days in a week and much less traffic flows compare to workdays, we have neglected this effect of weekends for simplicity.

Bottom Line: Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area.We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network.This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area.

View Article: PubMed Central - PubMed

Affiliation: Department of Evolutionary Studies of Biosystems (Sokendai-Hayama), The Graduate University for Advanced Studies (Sokendai), Hayama, Kanagawa, Japan; Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo, Japan.

ABSTRACT
An understanding of epidemiological dynamics is important for prevention and control of epidemic outbreaks. However, previous studies tend to focus only on specific areas, indicating that application to another area or intervention strategy requires a similar time-consuming simulation. Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area. The model is formulated on the basis of a metapopulation network in which local populations are interconnected by actual commuter flows in the Tokyo metropolitan area and the spread of infection is simulated by an individual-based model. We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network. Moreover, there is a strong relation between the population size and the time that the epidemic reaches this local population and we are able to determine the reason for this relation as well as its dependence on the commute network structure and epidemic parameters. This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area. Moreover, the clear relation of the time taken by the epidemic to reach each local population can be used as a novel measure for intervention; this enables efficient intervention strategies in each local population prior to the actual arrival.

Show MeSH
Related in: MedlinePlus