Suppression of epidemic outbreaks with heavy-tailed contact dynamics

We study the epidemic spreading process following contact dynamics with heavy-tailed waiting time distributions. We show both analytically and numerically that the temporal heterogeneity of contact dynamics can significantly suppress the disease's transmissibility, hence the size of epidemic outbreak, obstructing the spreading process. Furthermore, when the temporal heterogeneity is strong enough, one obtains the vanishing transmissibility for any finite recovery time and regardless of the underlying structure of contacts, the condition of which was derived.

[1]  Sergio Gómez,et al.  Nonperturbative heterogeneous mean-field approach to epidemic spreading in complex networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  K. Tamura,et al.  Metabolic engineering of plant alkaloid biosynthesis. Proc Natl Acad Sci U S A , 2001 .

[3]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[4]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[5]  D. Sornette.  Physics and financial economics (1776–2014): puzzles, Ising and agent-based models , 2014, Reports on progress in physics. Physical Society.

[6]  Adilson E. Motter,et al.  A Poissonian explanation for heavy tails in e-mail communication , 2008, Proceedings of the National Academy of Sciences.

[7]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[8]  Charles M. Grinstead,et al.  Introduction to probability , 1986, Statistics for the Behavioural Sciences.

[9]  P. V. Mieghem,et al.  Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks , 2013 .

[10]  A. Barabasi,et al.  Impact of non-Poissonian activity patterns on spreading processes. , 2006, Physical review letters.

[11]  Jean-Charles Delvenne,et al.  Burstiness and spreading on temporal networks , 2013, ArXiv.

[12]  Esteban Moro,et al.  Impact of human activity patterns on the dynamics of information diffusion. , 2009, Physical review letters.

[13]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[14]  Joel C. Miller,et al.  Epidemic size and probability in populations with heterogeneous infectivity and susceptibility. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Claudio Castellano,et al.  Thresholds for epidemic spreading in networks , 2010, Physical review letters.

[16]  Alexei Vazquez,et al.  Polynomial growth in branching processes with diverging reproductive number. , 2006, Physical review letters.

[17]  J. Muendel.  Epidemics and History: Disease, Power and Imperialism , 1998 .

[18]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[19]  K. Goh,et al.  Spreading dynamics following bursty human activity patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Albert-László Barabási,et al.  Modeling bursts and heavy tails in human dynamics , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Esteban Moro Egido,et al.  The dynamical strength of social ties in information spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  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 .

[24]  Pyoung-Seop Shim,et al.  Epidemic threshold of the susceptible-infected-susceptible model on complex networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[26]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[27]  S. Watts.  Epidemics and History: Disease, Power and Imperialism , 1997 .

[28]  Sergey N. Dorogovtsev,et al.  Localization and Spreading of Diseases in Complex Networks , 2012, Physical review letters.

[29]  J. Robins,et al.  Second look at the spread of epidemics on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.