Epidemic reemergence in adaptive complex networks.

The dynamic nature of a system gives rise to dynamical features of epidemic spreading, such as oscillation and bistability. In this paper, by studying the epidemic spreading in growing networks, in which susceptible nodes may adaptively break the connections with infected ones yet avoid being isolated, we reveal a phenomenon, epidemic reemergence, where the number of infected nodes is incubated at a low level for a long time and then erupts for a short time. The process may repeat several times before the infection finally vanishes. Simulation results show that all three factors, namely the network growth, the connection breaking, and the isolation avoidance, are necessary for epidemic reemergence to happen. We present a simple theoretical analysis to explain the process of reemergence in detail. Our study may offer some useful insights, helping explain the phenomenon of repeated epidemic explosions.

[1]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[2]  D. Cummings,et al.  Strategies for containing an emerging influenza pandemic in Southeast Asia , 2005, Nature.

[3]  Marcel Salathé,et al.  Dynamics and Control of Diseases in Networks with Community Structure , 2010, PLoS Comput. Biol..

[4]  Michael Szell,et al.  Multirelational organization of large-scale social networks in an online world , 2010, Proceedings of the National Academy of Sciences.

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

[6]  N A M Araújo,et al.  Explosive Percolation Via Control of the Largest Cluster , 2010, Physical review letters.

[7]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[8]  Yukio Hayashi,et al.  Oscillatory epidemic prevalence in growing scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[10]  Shlomo Havlin,et al.  Finding a better immunization strategy. , 2008, Physical review letters.

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

[12]  Jesús Gómez-Gardeñes,et al.  Annealed and mean-field formulations of disease dynamics on static and adaptive networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

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

[15]  José S Andrade,et al.  Tricritical point in explosive percolation. , 2010, Physical review letters.

[16]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[18]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[19]  C. Macken,et al.  Mitigation strategies for pandemic influenza in the United States. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[20]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[21]  George H. Weiss,et al.  On the asymptotic behavior of the stochastic and deterministic models of an epidemic , 1971 .

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  Ira B Schwartz,et al.  Enhanced vaccine control of epidemics in adaptive networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  A. J. Hall.  Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[26]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[27]  B. M. Fulk.  MATH , 1992 .

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

[29]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.