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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 intercept and slope of the linear relationship between the arriving time of epidemic and logarithmic local population size.The intercept (A1–2) and slope (A3–4) of linear regression line for the arrival time of epidemic, and the corresponding results calculated from the exponential growth approximation of the linearized population size class model (B1–2) and (B3–4), respectively (see main text for details of approximation) are shown. The results are plotted as the functions of infection rate and the color of each line indicates the sum of the population sizes of the initially infected home and work populations. (A1–4): regression coefficient statistically estimated from the results of the individual-based model (IBM) simulations. (A1) and (A2): estimated intercepts  and , respectively. (A3) and (A4): estimated (sign reversed) slopes  and , respectively. All regressions were statistically significant according to the P-value of the regression coefficient ().
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pone-0098518-g007: The intercept and slope of the linear relationship between the arriving time of epidemic and logarithmic local population size.The intercept (A1–2) and slope (A3–4) of linear regression line for the arrival time of epidemic, and the corresponding results calculated from the exponential growth approximation of the linearized population size class model (B1–2) and (B3–4), respectively (see main text for details of approximation) are shown. The results are plotted as the functions of infection rate and the color of each line indicates the sum of the population sizes of the initially infected home and work populations. (A1–4): regression coefficient statistically estimated from the results of the individual-based model (IBM) simulations. (A1) and (A2): estimated intercepts and , respectively. (A3) and (A4): estimated (sign reversed) slopes and , respectively. All regressions were statistically significant according to the P-value of the regression coefficient ().

Mentions: The arrival time of the epidemic in each local population is shown in Figure 6B1–2; each point represents the mean value across the ensemble of Monte Carlo simulations in which a global epidemic occurred. Similar results obtained by deterministic PSCM are given in Figure 6B3. For both home and work populations, a larger population size is associated with faster arrival time of the epidemic. Moreover, the arrival time of the epidemic clearly depends on the local population size i.e., it decreases in a linear manner on a semi-logarithmic plot: and for the -th home population and -th work population, respectively. The regression coefficients are: for home populations, intercept ( confidence interval, CI) and slope ( CI) (coefficient of determination: ); and for work populations, intercept ( CI) and slope ( CI) (coefficient of determination: ). Roughly speaking, increasing the local population size 3-fold causes the epidemic to arrive 2 days earlier, and infection of a work population lags that of a similar-sized home population by approximately 4 days. These results show a strong statistical relation between the arrival time of an epidemic in a local population and the size of that population. Figures 7A1–2 and 7A3–4 show how the intercepts ( and ) and the slopes ( and ) of the regression depend on the infection rate and the size of the initially infected population. In both home and work populations, the intercept decreases as the infection rate increases (Figure 7A1–2). The slope also decreases with the infection rate (Figure 7A3–4), indicating that the dependence on the local population size is weaker when the infection rate is sufficiently large. The intercepts (Figure 7A1–2) but not the slopes (Figure 7A3–4) depend on the sizes of the initial home and work populations. The intercept depends especially on the sum of the population sizes of initial home and work populations; as this sum increases, the intercept decreases, signifying an earlier overall arrival time of the epidemic (Figure 7A1–2).


Epidemic process over the commute network in a metropolitan area.

Yashima K, Sasaki A - PLoS ONE (2014)

The intercept and slope of the linear relationship between the arriving time of epidemic and logarithmic local population size.The intercept (A1–2) and slope (A3–4) of linear regression line for the arrival time of epidemic, and the corresponding results calculated from the exponential growth approximation of the linearized population size class model (B1–2) and (B3–4), respectively (see main text for details of approximation) are shown. The results are plotted as the functions of infection rate and the color of each line indicates the sum of the population sizes of the initially infected home and work populations. (A1–4): regression coefficient statistically estimated from the results of the individual-based model (IBM) simulations. (A1) and (A2): estimated intercepts  and , respectively. (A3) and (A4): estimated (sign reversed) slopes  and , respectively. All regressions were statistically significant according to the P-value of the regression coefficient ().
© Copyright Policy
Related In: Results  -  Collection

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

pone-0098518-g007: The intercept and slope of the linear relationship between the arriving time of epidemic and logarithmic local population size.The intercept (A1–2) and slope (A3–4) of linear regression line for the arrival time of epidemic, and the corresponding results calculated from the exponential growth approximation of the linearized population size class model (B1–2) and (B3–4), respectively (see main text for details of approximation) are shown. The results are plotted as the functions of infection rate and the color of each line indicates the sum of the population sizes of the initially infected home and work populations. (A1–4): regression coefficient statistically estimated from the results of the individual-based model (IBM) simulations. (A1) and (A2): estimated intercepts and , respectively. (A3) and (A4): estimated (sign reversed) slopes and , respectively. All regressions were statistically significant according to the P-value of the regression coefficient ().
Mentions: The arrival time of the epidemic in each local population is shown in Figure 6B1–2; each point represents the mean value across the ensemble of Monte Carlo simulations in which a global epidemic occurred. Similar results obtained by deterministic PSCM are given in Figure 6B3. For both home and work populations, a larger population size is associated with faster arrival time of the epidemic. Moreover, the arrival time of the epidemic clearly depends on the local population size i.e., it decreases in a linear manner on a semi-logarithmic plot: and for the -th home population and -th work population, respectively. The regression coefficients are: for home populations, intercept ( confidence interval, CI) and slope ( CI) (coefficient of determination: ); and for work populations, intercept ( CI) and slope ( CI) (coefficient of determination: ). Roughly speaking, increasing the local population size 3-fold causes the epidemic to arrive 2 days earlier, and infection of a work population lags that of a similar-sized home population by approximately 4 days. These results show a strong statistical relation between the arrival time of an epidemic in a local population and the size of that population. Figures 7A1–2 and 7A3–4 show how the intercepts ( and ) and the slopes ( and ) of the regression depend on the infection rate and the size of the initially infected population. In both home and work populations, the intercept decreases as the infection rate increases (Figure 7A1–2). The slope also decreases with the infection rate (Figure 7A3–4), indicating that the dependence on the local population size is weaker when the infection rate is sufficiently large. The intercepts (Figure 7A1–2) but not the slopes (Figure 7A3–4) depend on the sizes of the initial home and work populations. The intercept depends especially on the sum of the population sizes of initial home and work populations; as this sum increases, the intercept decreases, signifying an earlier overall arrival time of the epidemic (Figure 7A1–2).

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