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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 of epidemic and the arrival time of epidemic at local populations.The final size of the local epidemic (A) and the time until the infected individuals first appear in the local population (B) (i.e., the arrival time of epidemic) plotted against the local population size. The population size is on a logarithmic scale. (A1–2) and (B1–2): results of the individual-based model (IBM) simulations; each point (dots) gives the mean value of the Monte Carlo ensemble averaged over 100 Monte Carlo runs for each local population, and the blue and red dots correspond to the results for the home and work populations, respectively. The black lines in (A1–2) give the mean value of the final size of the local epidemic for each population size class. The black lines in (B1–2) represent the regression line of the arrival time of the epidemic in the local population versus the logarithm of the population size. The regression line for the arrival time  in the -th home population with population size , , was highly significant, with a P-value of  in the  test ( with the degrees of freedom (1, 1084)), . The estimated intercept  and slope  and their  confidence intervals (CIs) are  ( CI) and  ( CI). The same was true for the arrival times in the work population; the regression  was highly significant (,  with ), with estimated intercept and slope  ( CI) and  ( CI), respectively. (A3) and (B3): corresponding results obtained from the population size class model (PSCM); the blue line shows the result for the home population and the red line the result for the work population (refer main text for details). The infection rate was . A person commuting from “Gyotoku” station to “Aoyama-itchome” station was designated the initially infectious individual.
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pone-0098518-g006: The final size of epidemic and the arrival time of epidemic at local populations.The final size of the local epidemic (A) and the time until the infected individuals first appear in the local population (B) (i.e., the arrival time of epidemic) plotted against the local population size. The population size is on a logarithmic scale. (A1–2) and (B1–2): results of the individual-based model (IBM) simulations; each point (dots) gives the mean value of the Monte Carlo ensemble averaged over 100 Monte Carlo runs for each local population, and the blue and red dots correspond to the results for the home and work populations, respectively. The black lines in (A1–2) give the mean value of the final size of the local epidemic for each population size class. The black lines in (B1–2) represent the regression line of the arrival time of the epidemic in the local population versus the logarithm of the population size. The regression line for the arrival time in the -th home population with population size , , was highly significant, with a P-value of in the test ( with the degrees of freedom (1, 1084)), . The estimated intercept and slope and their confidence intervals (CIs) are ( CI) and ( CI). The same was true for the arrival times in the work population; the regression was highly significant (, with ), with estimated intercept and slope ( CI) and ( CI), respectively. (A3) and (B3): corresponding results obtained from the population size class model (PSCM); the blue line shows the result for the home population and the red line the result for the work population (refer main text for details). The infection rate was . A person commuting from “Gyotoku” station to “Aoyama-itchome” station was designated the initially infectious individual.

Mentions: The final size of the local epidemic within each population is shown in Figures 6A1–2; each dot represents the mean value across the ensemble of the Monte Carlo simulations in which a global epidemic occurred. In both home and work populations, larger populations have larger final local epidemic sizes. In sufficiently large work populations (exceeding commuters), almost all of the commuters within the local home population are infected, whereas in sufficiently small work populations (less than commuters), only approximately of the commuters within the local work population are infected. The final size of the local epidemic is larger in home populations than in work populations of the same size. Moreover, we found that the final size of the local epidemic in both home and work populations depends strongly on the infection rate and the size of the local population but negligibly on the sizes of the initial home and work populations. The deterministic PSCM exhibited qualitatively similar dependencies, although the final sizes of the local epidemics are slightly smaller (Figure 6A3). Therefore, the local population size alone is sufficient to predict the total damage caused by an epidemic in a local population.


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

The final size of epidemic and the arrival time of epidemic at local populations.The final size of the local epidemic (A) and the time until the infected individuals first appear in the local population (B) (i.e., the arrival time of epidemic) plotted against the local population size. The population size is on a logarithmic scale. (A1–2) and (B1–2): results of the individual-based model (IBM) simulations; each point (dots) gives the mean value of the Monte Carlo ensemble averaged over 100 Monte Carlo runs for each local population, and the blue and red dots correspond to the results for the home and work populations, respectively. The black lines in (A1–2) give the mean value of the final size of the local epidemic for each population size class. The black lines in (B1–2) represent the regression line of the arrival time of the epidemic in the local population versus the logarithm of the population size. The regression line for the arrival time  in the -th home population with population size , , was highly significant, with a P-value of  in the  test ( with the degrees of freedom (1, 1084)), . The estimated intercept  and slope  and their  confidence intervals (CIs) are  ( CI) and  ( CI). The same was true for the arrival times in the work population; the regression  was highly significant (,  with ), with estimated intercept and slope  ( CI) and  ( CI), respectively. (A3) and (B3): corresponding results obtained from the population size class model (PSCM); the blue line shows the result for the home population and the red line the result for the work population (refer main text for details). The infection rate was . A person commuting from “Gyotoku” station to “Aoyama-itchome” station was designated the initially infectious individual.
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Related In: Results  -  Collection

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

pone-0098518-g006: The final size of epidemic and the arrival time of epidemic at local populations.The final size of the local epidemic (A) and the time until the infected individuals first appear in the local population (B) (i.e., the arrival time of epidemic) plotted against the local population size. The population size is on a logarithmic scale. (A1–2) and (B1–2): results of the individual-based model (IBM) simulations; each point (dots) gives the mean value of the Monte Carlo ensemble averaged over 100 Monte Carlo runs for each local population, and the blue and red dots correspond to the results for the home and work populations, respectively. The black lines in (A1–2) give the mean value of the final size of the local epidemic for each population size class. The black lines in (B1–2) represent the regression line of the arrival time of the epidemic in the local population versus the logarithm of the population size. The regression line for the arrival time in the -th home population with population size , , was highly significant, with a P-value of in the test ( with the degrees of freedom (1, 1084)), . The estimated intercept and slope and their confidence intervals (CIs) are ( CI) and ( CI). The same was true for the arrival times in the work population; the regression was highly significant (, with ), with estimated intercept and slope ( CI) and ( CI), respectively. (A3) and (B3): corresponding results obtained from the population size class model (PSCM); the blue line shows the result for the home population and the red line the result for the work population (refer main text for details). The infection rate was . A person commuting from “Gyotoku” station to “Aoyama-itchome” station was designated the initially infectious individual.
Mentions: The final size of the local epidemic within each population is shown in Figures 6A1–2; each dot represents the mean value across the ensemble of the Monte Carlo simulations in which a global epidemic occurred. In both home and work populations, larger populations have larger final local epidemic sizes. In sufficiently large work populations (exceeding commuters), almost all of the commuters within the local home population are infected, whereas in sufficiently small work populations (less than commuters), only approximately of the commuters within the local work population are infected. The final size of the local epidemic is larger in home populations than in work populations of the same size. Moreover, we found that the final size of the local epidemic in both home and work populations depends strongly on the infection rate and the size of the local population but negligibly on the sizes of the initial home and work populations. The deterministic PSCM exhibited qualitatively similar dependencies, although the final sizes of the local epidemics are slightly smaller (Figure 6A3). Therefore, the local population size alone is sufficient to predict the total damage caused by an epidemic in a local 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