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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 final size and the peak time of global epidemic.The final size of the global epidemic (A) and the time until an epidemic initiated by a single host reaches its peak (B) plotted against the infection rate . (A1) and (B1): results observed in the individual-based model (IBM) simulations; each point gives the Monte Carlo ensemble average value corresponding to different epidemic parameters, and the color indicates the sum of the sizes of the initially infected home and work populations. Here, the cases for initial extinction of disease are excluded from the ensemble. (A2) and (B2): corresponding results from the population size class model (PSCM) calculations.
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pone-0098518-g005: The final size and the peak time of global epidemic.The final size of the global epidemic (A) and the time until an epidemic initiated by a single host reaches its peak (B) plotted against the infection rate . (A1) and (B1): results observed in the individual-based model (IBM) simulations; each point gives the Monte Carlo ensemble average value corresponding to different epidemic parameters, and the color indicates the sum of the sizes of the initially infected home and work populations. Here, the cases for initial extinction of disease are excluded from the ensemble. (A2) and (B2): corresponding results from the population size class model (PSCM) calculations.

Mentions: The final size of the global epidemic as a function of the infection rate is shown in Figure 5A1; each point corresponds to a different set of initial home and work populations and represents the mean value across the ensemble of Monte Carlo simulations in which a global epidemic occurred. In Figure 5A1, the final sizes of the global epidemics for a given infection rate are concentrated to a single point, which implies that once a global epidemic is underway, its final size is almost independent of the initial home and work population sizes. This contrasts sharply with our result for the probability of a global epidemic, which is quite sensitive to the sizes of the initial home and work populations. For , although a global epidemic did occur, its final size remained very low and only a small percentage of the population is infected. As the infection rate increases, the final size of the global epidemic increases until it approaches 1, meaning that almost all individuals in the population are infected, at around . As the figure shows, the infection rate had a threshold value , approximately at , below which global invasion of the epidemic could not occur. At this critical value of the infection rate, the local basic reproductive ratio (i.e., the single population basic reproduction ratio ) in the Shinjuku station area (the largest work station) is 1.083, which is only slightly greater than 1. In contrast, the local basic reproductive ratio for the critical infection rate in the Oizumu-gakuen station area, the largest home population, is much lower than 1 (0.17). When we considered the mean rather than the largest population sizes, the local basic reproductive ratio for the critical infection rate was just 0.217 in the mean work population and was even smaller, 0.0546, in the mean home population. This suggests that a few very large work populations can play a pivotal role in an epidemic outbreak in the Tokyo metropolitan area.


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

The final size and the peak time of global epidemic.The final size of the global epidemic (A) and the time until an epidemic initiated by a single host reaches its peak (B) plotted against the infection rate . (A1) and (B1): results observed in the individual-based model (IBM) simulations; each point gives the Monte Carlo ensemble average value corresponding to different epidemic parameters, and the color indicates the sum of the sizes of the initially infected home and work populations. Here, the cases for initial extinction of disease are excluded from the ensemble. (A2) and (B2): corresponding results from the population size class model (PSCM) calculations.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0098518-g005: The final size and the peak time of global epidemic.The final size of the global epidemic (A) and the time until an epidemic initiated by a single host reaches its peak (B) plotted against the infection rate . (A1) and (B1): results observed in the individual-based model (IBM) simulations; each point gives the Monte Carlo ensemble average value corresponding to different epidemic parameters, and the color indicates the sum of the sizes of the initially infected home and work populations. Here, the cases for initial extinction of disease are excluded from the ensemble. (A2) and (B2): corresponding results from the population size class model (PSCM) calculations.
Mentions: The final size of the global epidemic as a function of the infection rate is shown in Figure 5A1; each point corresponds to a different set of initial home and work populations and represents the mean value across the ensemble of Monte Carlo simulations in which a global epidemic occurred. In Figure 5A1, the final sizes of the global epidemics for a given infection rate are concentrated to a single point, which implies that once a global epidemic is underway, its final size is almost independent of the initial home and work population sizes. This contrasts sharply with our result for the probability of a global epidemic, which is quite sensitive to the sizes of the initial home and work populations. For , although a global epidemic did occur, its final size remained very low and only a small percentage of the population is infected. As the infection rate increases, the final size of the global epidemic increases until it approaches 1, meaning that almost all individuals in the population are infected, at around . As the figure shows, the infection rate had a threshold value , approximately at , below which global invasion of the epidemic could not occur. At this critical value of the infection rate, the local basic reproductive ratio (i.e., the single population basic reproduction ratio ) in the Shinjuku station area (the largest work station) is 1.083, which is only slightly greater than 1. In contrast, the local basic reproductive ratio for the critical infection rate in the Oizumu-gakuen station area, the largest home population, is much lower than 1 (0.17). When we considered the mean rather than the largest population sizes, the local basic reproductive ratio for the critical infection rate was just 0.217 in the mean work population and was even smaller, 0.0546, in the mean home population. This suggests that a few very large work populations can play a pivotal role in an epidemic outbreak in the Tokyo metropolitan area.

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