Epidemic process over the commute network in a metropolitan area.

Kenta Yashima,Akira Sasaki,Jack Anthony Gilbert

doi:10.1371/journal.pone.0098518

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.

Highlights

A theoretical understanding of the epidemic spread of an infectious disease within a metropolitan area is essential for its prevention and control
Commute network data for the Tokyo metropolitan area The data on commuter flow within the Tokyo metropolitan area were obtained from the Urban Transportation Census (UTC) [19], a survey conducted by the Japanese Ministry of Land, Infrastructure, Transport and Tourism that has been carried out every 5 years since 1960 at three major metropolitan areas of Japan, which are Tokyo, Nagoya, and Osaka regions
Probability of a global epidemic The probability of a global epidemic PG is defined as the fraction of the independent runs of the Monte Carlo simulation in which a global epidemic occurred (i.e., PG~nG=nM, where nG denotes the number of global epidemics observed within nM runs of the Monte Carlo simulation; refer to Section Individual-based model: Epidemic dynamics for a more detailed definition of a global epidemic)

Summary

Introduction

A theoretical understanding of the epidemic spread of an infectious disease within a metropolitan area is essential for its prevention and control. We focus on such theoretical aspects as how the epidemiological parameters and statistical properties of the commute network affect the probability that an infectious disease invades and spreads out globally throughout the area, the final size of the global epidemic, and the time until the epidemic attains its peak, as these aspects would provide valuable insights into the prevention and control of a disease within a metropolitan area For this purpose, we simulated the spread of infection over the commute network in the Tokyo metropolitan area using an individual-based model (IBM) in which each individual’s daily commute movements are simulated on the basis of the actual commute data for the Tokyo metropolitan area. Yasuda et al [7,8] and Saito et al [9] performed a similar analysis based on actual demographic data by constructing a suburban community along a commuter line These studies aimed to analyze the outcomes of various intervention strategies in each specific scenario and evaluate their efficacies quantitatively to form a basis for policy-making. A more general understanding of the effects of the geographic and social structures of the population on the epidemic dynamics is needed

Methods

Results

Conclusion