How dynamic social activity shapes COVID-19 epidemic: waves, plateaus, and endemic state.

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the consequences of dynamic heterogeneity. We integrate the stochastic dynamics of social activity into traditional epidemiological models. The overall epidemic dynamics is condensed to three differential equations and is characterized by an emergent long timescale. Our model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves. Individual waves are suppressed at the state of Transient Collective Immunity (TCI), which subsequently degrades due to the dynamic nature of social activity. Our results also provide a new mechanism for emerging pathogens to transition from a fast-paced epidemic to the endemic state.

[1]  Zachary J. Weiner,et al.  Persistent heterogeneity not short-term overdispersion determines herd immunity to COVID-19 , 2020, medRxiv.

[2]  Sang Woo Park,et al.  Awareness-driven behavior changes can shift the shape of epidemics away from peaks and toward plateaus, shoulders, and oscillations , 2020, Proceedings of the National Academy of Sciences of the United States of America.

[3]  C. Aschwanden.  The false promise of herd immunity for COVID-19 , 2020, Nature.

[4]  Stefan Thurner,et al.  A network-based explanation of why most COVID-19 infection curves are linear , 2020, Proceedings of the National Academy of Sciences.

[5]  A. Vespignani,et al.  Transmission heterogeneities, kinetics, and controllability of SARS-CoV-2 , 2020, medRxiv.

[6]  F. Jülicher,et al.  Power-law population heterogeneity governs epidemic waves , 2020, PloS one.

[7]  M. Gomes,et al.  Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics , 2020, medRxiv.

[8]  Frank Ball,et al.  A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2 , 2020, Science.

[9]  B. F. Nielsen,et al.  Heterogeneity is essential for contact tracing , 2020, medRxiv.

[10]  Andrew J. Medford,et al.  Heterogeneity in susceptibility dictates the order of epidemiological models , 2020 .

[11]  Caetano Souto-Maior,et al.  Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold , 2020, medRxiv.

[12]  Sebastian Funk,et al.  Extended data: Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China , 2020 .

[13]  R. Neher,et al.  Potential impact of seasonal forcing on a SARS-CoV-2 pandemic , 2020, medRxiv.

[14]  Srijan Sengupta,et al.  Toward epidemic thresholds on temporal networks: a review and open questions , 2019, Applied Network Science.

[15]  Alain Barrat,et al.  Simplicial Activity Driven Model. , 2018, Physical review letters.

[16]  Ciro Cattuto,et al.  Robust modeling of human contact networks across different scales and proximity-sensing techniques , 2017, SocInfo.

[17]  Jari Saramäki,et al.  From seconds to months: an overview of multi-scale dynamics of mobile telephone calls , 2015, The European Physical Journal B.

[18]  Shweta Bansal,et al.  Eight challenges for network epidemic models. , 2015, Epidemics.

[19]  Mattia Frasca,et al.  Effect of individual behavior on epidemic spreading in activity-driven networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[21]  V. Colizza,et al.  Analytical computation of the epidemic threshold on temporal networks , 2014, 1406.4815.

[22]  Matt J. Keeling,et al.  Social encounter networks: characterizing Great Britain , 2013, Proceedings of the Royal Society B: Biological Sciences.

[23]  P. Holme,et al.  Predicting and controlling infectious disease epidemics using temporal networks , 2013, F1000prime reports.

[24]  J. Slingenbergh,et al.  Pathogen–host–environment interplay and disease emergence , 2013, Emerging Microbes & Infections.

[25]  G. Katriel.  The size of epidemics in populations with heterogeneous susceptibility , 2012, Journal of mathematical biology.

[26]  Joel C. Miller,et al.  A Note on the Derivation of Epidemic Final Sizes , 2012, Bulletin of mathematical biology.

[27]  R. Pastor-Satorras,et al.  Activity driven modeling of time varying networks , 2012, Scientific Reports.

[28]  Shweta Bansal,et al.  The dynamic nature of contact networks in infectious disease epidemiology , 2010, Journal of biological dynamics.

[29]  S. Havlin,et al.  Scaling laws of human interaction activity , 2009, Proceedings of the National Academy of Sciences.

[30]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[31]  W. Edmunds,et al.  Dynamic social networks and the implications for the spread of infectious disease , 2008, Journal of The Royal Society Interface.

[32]  A. Novozhilov.  On the spread of epidemics in a closed heterogeneous population. , 2008, Mathematical biosciences.

[33]  L. Meyers,et al.  Susceptible–infected–recovered epidemics in dynamic contact networks , 2007, Proceedings of the Royal Society B: Biological Sciences.

[34]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[35]  L. Meyers,et al.  When individual behaviour matters: homogeneous and network models in epidemiology , 2007, Journal of The Royal Society Interface.

[36]  Nathan D. Wolfe,et al.  Origins of major human infectious diseases , 2007, Nature.

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

[38]  M. Small,et al.  Super-spreaders and the rate of transmission of the SARS virus , 2006, Physica D: Nonlinear Phenomena.

[39]  P. E. Kopp,et al.  Superspreading and the effect of individual variation on disease emergence , 2005, Nature.

[40]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[41]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[42]  M. Newman,et al.  Network theory and SARS: predicting outbreak diversity , 2004, Journal of Theoretical Biology.

[43]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[44]  A. Schuchat,et al.  Superspreading SARS Events, Beijing, 2003 , 2004, Emerging infectious diseases.

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

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

[47]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[48]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[51]  R. May,et al.  Epidemiology. How viruses spread among computers and people. , 2001, Science.

[52]  W. Feller.  TWO SINGULAR DIFFUSION PROBLEMS , 1951 .