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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 that a single infected host causes global epidemic.The probability of a global epidemic, , as a function of the home population size (horizontal axis; initial home population) and work population size (vertical axis; initial work population) of the initially infected host for various infection rate . (A1–4) The results of the individual-based model (IBM) simulations of the spread of infectious disease over the commute network of the Tokyo metropolitan area which starts with a single infectious individual commuting from a randomly chosen home population to a randomly chosen work population. Each panel corresponds to a different infection rate, and the population sizes are plotted on logarithmic scales. (B1–4) The corresponding results obtained using a branching process formula in the population size class model (PSCM). (C1–4) The corresponding results of the IBM simulations using the random reconnection model (RRM). In each panel, the contour plot represents interpolation of the results calculated using the data of 184 combinations of initial home and work population sizes.
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pone-0098518-g003: The probability that a single infected host causes global epidemic.The probability of a global epidemic, , as a function of the home population size (horizontal axis; initial home population) and work population size (vertical axis; initial work population) of the initially infected host for various infection rate . (A1–4) The results of the individual-based model (IBM) simulations of the spread of infectious disease over the commute network of the Tokyo metropolitan area which starts with a single infectious individual commuting from a randomly chosen home population to a randomly chosen work population. Each panel corresponds to a different infection rate, and the population sizes are plotted on logarithmic scales. (B1–4) The corresponding results obtained using a branching process formula in the population size class model (PSCM). (C1–4) The corresponding results of the IBM simulations using the random reconnection model (RRM). In each panel, the contour plot represents interpolation of the results calculated using the data of 184 combinations of initial home and work population sizes.

Mentions: The probability of a global epidemic is defined as the fraction of the independent runs of the Monte Carlo simulation in which a global epidemic occurred (i.e., , where denotes the number of global epidemics observed within runs of the Monte Carlo simulation; refer to Section Individual-based model: Epidemic dynamics for a more detailed definition of a global epidemic). The probability of a global epidemic observed in the IBM simulation for a given infection rate and sizes of the home and work populations of the initial infected host is plotted in Figure 3A. When the infection rate is low, initial extinction of the disease prevails over the global epidemic in an initially infected population of any size (Figure 3A1). However, when the infection rate is sufficiently high (Figures 3A2–4), increases with the sizes of either initial home or work population.


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

The probability that a single infected host causes global epidemic.The probability of a global epidemic, , as a function of the home population size (horizontal axis; initial home population) and work population size (vertical axis; initial work population) of the initially infected host for various infection rate . (A1–4) The results of the individual-based model (IBM) simulations of the spread of infectious disease over the commute network of the Tokyo metropolitan area which starts with a single infectious individual commuting from a randomly chosen home population to a randomly chosen work population. Each panel corresponds to a different infection rate, and the population sizes are plotted on logarithmic scales. (B1–4) The corresponding results obtained using a branching process formula in the population size class model (PSCM). (C1–4) The corresponding results of the IBM simulations using the random reconnection model (RRM). In each panel, the contour plot represents interpolation of the results calculated using the data of 184 combinations of initial home and work population sizes.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0098518-g003: The probability that a single infected host causes global epidemic.The probability of a global epidemic, , as a function of the home population size (horizontal axis; initial home population) and work population size (vertical axis; initial work population) of the initially infected host for various infection rate . (A1–4) The results of the individual-based model (IBM) simulations of the spread of infectious disease over the commute network of the Tokyo metropolitan area which starts with a single infectious individual commuting from a randomly chosen home population to a randomly chosen work population. Each panel corresponds to a different infection rate, and the population sizes are plotted on logarithmic scales. (B1–4) The corresponding results obtained using a branching process formula in the population size class model (PSCM). (C1–4) The corresponding results of the IBM simulations using the random reconnection model (RRM). In each panel, the contour plot represents interpolation of the results calculated using the data of 184 combinations of initial home and work population sizes.
Mentions: The probability of a global epidemic is defined as the fraction of the independent runs of the Monte Carlo simulation in which a global epidemic occurred (i.e., , where denotes the number of global epidemics observed within runs of the Monte Carlo simulation; refer to Section Individual-based model: Epidemic dynamics for a more detailed definition of a global epidemic). The probability of a global epidemic observed in the IBM simulation for a given infection rate and sizes of the home and work populations of the initial infected host is plotted in Figure 3A. When the infection rate is low, initial extinction of the disease prevails over the global epidemic in an initially infected population of any size (Figure 3A1). However, when the infection rate is sufficiently high (Figures 3A2–4), increases with the sizes of either initial home or work population.

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