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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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The probability of global epidemic as a function of the basic reproductive ratios in the initially infected home and work populations.The probability of a global epidemic observed in the individual-based model (IBM) simulations based on the commute network data for the Tokyo metropolitan area plotted as a function of , where the independent variable is the sum of the single population basic reproduction ratios of the initial home and work populations ( and : home and work population sizes of the initially infected individual, respectively). Each point corresponds to a different set of epidemic parameters, and the color represents the infection rate . Black line, the probability of a global epidemic in the single population model with population size , i.e., that from  (main text for details).
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pone-0098518-g004: The probability of global epidemic as a function of the basic reproductive ratios in the initially infected home and work populations.The probability of a global epidemic observed in the individual-based model (IBM) simulations based on the commute network data for the Tokyo metropolitan area plotted as a function of , where the independent variable is the sum of the single population basic reproduction ratios of the initial home and work populations ( and : home and work population sizes of the initially infected individual, respectively). Each point corresponds to a different set of epidemic parameters, and the color represents the infection rate . Black line, the probability of a global epidemic in the single population model with population size , i.e., that from (main text for details).

Mentions: The invasion condition can further be simplified by a careful inspection of the branching process recurrence formula of the stochastic PSCM. We find that the probability of a global epidemic defined in the branching process for the initial spread of the infection can be approximated as (Equation 6 in Section B of Supporting Information S1):(2)which depends only on the sizes and of the home and work populations, respectively, to which the initially infected host resides (the black line in Figure 4). As the basic reproduction ratio of a single homogeneous population with the population size is given by(3)the probability of a global epidemic in equation (2) coincides with the probability that the infection will occur in a single isolated population of size [18], [22]. Figure 4 shows the probability of a global epidemic observed in the IBM simulations (dots) for various infection rates (different colors) and home and work population sizes of the initially infectious host and . The probability of a global epidemic for different combinations of , , and can be plotted against , resulting in a single but indistinct band.


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

The probability of global epidemic as a function of the basic reproductive ratios in the initially infected home and work populations.The probability of a global epidemic observed in the individual-based model (IBM) simulations based on the commute network data for the Tokyo metropolitan area plotted as a function of , where the independent variable is the sum of the single population basic reproduction ratios of the initial home and work populations ( and : home and work population sizes of the initially infected individual, respectively). Each point corresponds to a different set of epidemic parameters, and the color represents the infection rate . Black line, the probability of a global epidemic in the single population model with population size , i.e., that from  (main text for details).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0098518-g004: The probability of global epidemic as a function of the basic reproductive ratios in the initially infected home and work populations.The probability of a global epidemic observed in the individual-based model (IBM) simulations based on the commute network data for the Tokyo metropolitan area plotted as a function of , where the independent variable is the sum of the single population basic reproduction ratios of the initial home and work populations ( and : home and work population sizes of the initially infected individual, respectively). Each point corresponds to a different set of epidemic parameters, and the color represents the infection rate . Black line, the probability of a global epidemic in the single population model with population size , i.e., that from (main text for details).
Mentions: The invasion condition can further be simplified by a careful inspection of the branching process recurrence formula of the stochastic PSCM. We find that the probability of a global epidemic defined in the branching process for the initial spread of the infection can be approximated as (Equation 6 in Section B of Supporting Information S1):(2)which depends only on the sizes and of the home and work populations, respectively, to which the initially infected host resides (the black line in Figure 4). As the basic reproduction ratio of a single homogeneous population with the population size is given by(3)the probability of a global epidemic in equation (2) coincides with the probability that the infection will occur in a single isolated population of size [18], [22]. Figure 4 shows the probability of a global epidemic observed in the IBM simulations (dots) for various infection rates (different colors) and home and work population sizes of the initially infectious host and . The probability of a global epidemic for different combinations of , , and can be plotted against , resulting in a single but indistinct band.

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