Arrival time statistics in global disease spread

Metapopulation models describing cities with different populations coupled by the travel of individuals are of great importance in the understanding of disease spread on a large scale. An important example is the Rvachev–Longini model which is widely used in computational epidemiology. Few analytical results are, however, available and, in particular, little is known about paths followed by epidemics and disease arrival times. We study the arrival time of a disease in a city as a function of the starting seed of the epidemics. We propose an analytical ansatz, test it in the case of a spread on the worldwide air-transportation network, and show that it predicts accurately the arrival order of a disease in worldwide cities.

[1]  L. A. Rvachev,et al.  A mathematical model for the global spread of influenza , 1985 .

[2]  M. Keeling,et al.  The effects of local spatial structure on epidemiological invasions , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[3]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[4]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[5]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[6]  N. Ferguson,et al.  Planning for smallpox outbreaks , 2003, Nature.

[7]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[8]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[9]  Alessandro Vespignani,et al.  Evolution and Structure of the Internet: A Statistical Physics Approach , 2004 .

[10]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[12]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Roger Guimerà,et al.  Modeling the world-wide airport network , 2004 .

[14]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[15]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[16]  Pascal Crépey,et al.  Epidemic variability in complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  A. Vespignani,et al.  The Modeling of Global Epidemics: Stochastic Dynamics and Predictability , 2006, Bulletin of mathematical biology.

[18]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[19]  H. Stanley,et al.  Optimal paths in complex networks with correlated weights: the worldwide airport network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[21]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[22]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.