A unified framework of mutual influence between two pathogens in multiplex networks.

There are many evidences to show that different pathogens may interplay each other and cause a variety of mutual influences of epidemics in multiplex networks, but it is still lack of a framework to unify all the different dynamic outcomes of the interactions between the pathogens. We here study this problem and first time present the concept of state-dependent infectious rate, in contrast to the constant infectious rate in previous studies. We consider a model consisting of a two-layered network with one pathogen on the first layer and the other on the second layer, and show that all the different influences between the two pathogens can be given by the different range of parameters in the infectious rates, which includes the cases of mutual enhancement, mutual suppression, and even initial cooperation (suppression) induced final suppression (acceleration). A theoretical analysis is present to explain the numerical results.

[1]  Michael Small,et al.  The impact of awareness on epidemic spreading in networks , 2012, Chaos.

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

[3]  Víctor M Eguíluz,et al.  Epidemic threshold in structured scale-free networks. , 2002, Physical review letters.

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

[5]  P. Grassberger,et al.  Outbreaks of coinfections: The critical role of cooperativity , 2013, 1307.2404.

[6]  Alessandro Vespignani,et al.  Multiscale mobility networks and the spatial spreading of infectious diseases , 2009, Proceedings of the National Academy of Sciences.

[7]  Sergei S. Pilyugin,et al.  The Role of Coinfection in Multidisease Dynamics , 2006, SIAM J. Appl. Math..

[8]  Zonghua Liu,et al.  Influence of dynamical condensation on epidemic spreading in scale-free networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  D. Zanette,et al.  Infection Spreading in a Population with Evolving Contacts , 2007, Journal of biological physics.

[10]  Alessandro Vespignani,et al.  Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. , 2007, Journal of theoretical biology.

[11]  Piet Van Mieghem,et al.  Generalized Epidemic Mean-Field Model for Spreading Processes Over Multilayer Complex Networks , 2013, IEEE/ACM Transactions on Networking.

[12]  Julie Netherland,et al.  AIDS-related risk among adolescent males who have sex with males, females, or both: evidence from a statewide survey. , 2002, American journal of public health.

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

[14]  Sebastian Funk,et al.  Interacting epidemics on overlay networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Zhongyuan Ruan,et al.  How the contagion at links influences epidemic spreading , 2013 .

[16]  Bambi Hu,et al.  Epidemic spreading in community networks , 2005 .

[17]  Pietro Liò,et al.  Risk perception in epidemic modeling. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[19]  Sergio Gómez,et al.  On the dynamical interplay between awareness and epidemic spreading in multiplex networks , 2013, Physical review letters.

[20]  Joel C Miller,et al.  Cocirculation of infectious diseases on networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[22]  A. Fauci,et al.  The challenge of emerging and re-emerging infectious diseases , 2004, Nature.

[23]  Harry Eugene Stanley,et al.  Quarantine generated phase transition in epidemic spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Marián Boguñá,et al.  Epidemic spreading on interconnected networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Antoine Allard,et al.  Modeling the dynamical interaction between epidemics on overlay networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  R. Pastor-Satorras,et al.  Bosonic reaction-diffusion processes on scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. Newman,et al.  Interacting Epidemics and Coinfection on Contact Networks , 2013, PloS one.

[28]  Alessandro Vespignani,et al.  Absence of epidemic threshold in scale-free networks with degree correlations. , 2002, Physical review letters.

[29]  S. Havlin,et al.  Epidemic threshold for the susceptible-infectious-susceptible model on random networks. , 2010, Physical review letters.

[30]  Zhongyuan Ruan,et al.  Epidemic spreading with information-driven vaccination. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Ana Perisic,et al.  Social Contact Networks and Disease Eradicability under Voluntary Vaccination , 2009, PLoS Comput. Biol..

[32]  Alessandro Vespignani,et al.  Invasion threshold in heterogeneous metapopulation networks. , 2007, Physical review letters.

[33]  Ira B Schwartz,et al.  Rewiring for adaptation. , 2010, Physics.

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

[35]  Lewi Stone,et al.  Unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[37]  Alessandro Vespignani,et al.  Efficiency and reliability of epidemic data dissemination in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Peter Grassberger,et al.  SIR epidemics with long-range infection in one dimension , 2012, 1212.5396.

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

[40]  H. Mills,et al.  Pathogen spread on coupled networks: effect of host and network properties on transmission thresholds. , 2013, Journal of theoretical biology.

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

[42]  B. Dodge,et al.  Male Bisexuality and Condom Use at Last Sexual Encounter: Results From a National Survey , 2007, Journal of sex research.

[43]  Harry Eugene Stanley,et al.  Epidemics on Interconnected Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Alex Arenas,et al.  Traffic-driven epidemic spreading in finite-size scale-free networks , 2009, Proceedings of the National Academy of Sciences.

[45]  M. Newman.  Threshold effects for two pathogens spreading on a network. , 2005, Physical review letters.

[46]  K Dietz,et al.  Epidemiologic interference of virus populations , 1979, Journal of mathematical biology.

[47]  Cláudia T. Codeço,et al.  Epigrass: a tool to study disease spread in complex networks. , 2007, Source Code for Biology and Medicine.

[48]  L. Hébert-Dufresne,et al.  Adaptive networks: Coevolution of disease and topology. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Zonghua Liu.  Effect of mobility in partially occupied complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[51]  M. Small,et al.  Hub nodes inhibit the outbreak of epidemic under voluntary vaccination , 2010 .

[52]  Zhongyuan Ruan,et al.  Explosive synchronization on co-evolving networks , 2013 .

[53]  Zhongyuan Ruan,et al.  Risks of an epidemic in a two-layered railway-local area traveling network , 2013, The European Physical Journal B.

[54]  Ming Tang,et al.  Epidemic spreading by objective traveling , 2009 .

[55]  J. Kublin,et al.  Dual Infection with HIV and Malaria Fuels the Spread of Both Diseases in Sub-Saharan Africa , 2006, Science.

[56]  Peter A Leone,et al.  Men Who Have Sex With Men and Women: A Unique Risk Group for HIV Transmission on North Carolina College Campuses , 2006, Sexually transmitted diseases.

[57]  Attila Rákos,et al.  Epidemic spreading in evolving networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[59]  W. L. Jeffries,et al.  The number of recent sex partners among bisexual men in the United States. , 2011, Perspectives on sexual and reproductive health.