Epidemic outbreak for an SIS model in multiplex networks with immunization.

With the aim of understanding epidemic spreading in a general multiplex network and designing optimal immunization strategies, a mathematical model based on multiple degree is built to analyze the threshold condition for epidemic outbreak. Two kinds of strategies, the multiplex node-based immunization and the layer node-based immunization, are examined. Theoretical results show that the general framework proposed here can illustrate the effect of diverse correlations and immunizations on the outbreak condition in multiplex networks. Under a set of conditions on uncorrelated coefficients, the specific epidemic thresholds are shown to be only dependent on the respective degree distribution in each layer.

[1]  Xiaogang Jin,et al.  Diversity of multilayer networks and its impact on collaborating epidemics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Ruyin Chen,et al.  Effect of external periodic regulations on Brownian motor , 2015 .

[3]  Faryad Darabi Sahneh,et al.  Effect of coupling on the epidemic threshold in interconnected complex networks: A spectral analysis , 2012, 2013 American Control Conference.

[4]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

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

[6]  Lidia A. Braunstein,et al.  Immunization strategy for epidemic spreading on multilayer networks , 2014, ArXiv.

[7]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

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

[9]  Yamir Moreno,et al.  Dynamics of interacting diseases , 2014, 1402.4523.

[10]  Xinchu Fu,et al.  Mean-field modeling approach for understanding epidemic dynamics in interconnected networks , 2015 .

[11]  Zhen Jin,et al.  Epidemic dynamics on semi-directed complex networks. , 2013, Mathematical biosciences.

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

[13]  M. Small,et al.  Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Ming Tang,et al.  Asymmetrically interacting spreading dynamics on complex layered networks , 2014, Scientific Reports.

[15]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Zengrong Liu,et al.  Mean-field level analysis of epidemics in directed networks , 2009 .

[17]  Michael Small,et al.  Threshold analysis of the susceptible-infected-susceptible model on overlay networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[18]  Xinchu Fu,et al.  Immunization and epidemic threshold of an SIS model in complex networks , 2016 .

[19]  Kwang-Il Goh,et al.  Towards real-world complexity: an introduction to multiplex networks , 2015, ArXiv.

[20]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  C. Scoglio,et al.  Competitive epidemic spreading over arbitrary multilayer networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Rowland R Kao,et al.  The effect of contact heterogeneity and multiple routes of transmission on final epidemic size. , 2006, Mathematical biosciences.

[23]  B. Bollobás.  The evolution of random graphs , 1984 .

[24]  Romualdo Pastor-Satorras,et al.  Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  N. Madar,et al.  Immunization and epidemic dynamics in complex networks , 2004 .

[26]  Dawei Zhao,et al.  Multiple routes transmitted epidemics on multiplex networks , 2013, ArXiv.

[27]  Alessandro Vespignani,et al.  Complex networks: The fragility of interdependency , 2010, Nature.

[28]  C. Buono,et al.  Epidemics in Partially Overlapped Multiplex Networks , 2013, PloS one.

[29]  M. Carlucci,et al.  Intraoperative Cardiac Arrest and Mortality in Trauma Patients. A 14-Yr Survey from a Brazilian Tertiary Teaching Hospital , 2014, PloS one.

[30]  Hang-Hyun Jo,et al.  Immunization dynamics on a two-layer network model , 2003, cond-mat/0310372.

[31]  J. Borge-Holthoefer,et al.  Discrete-time Markov chain approach to contact-based disease spreading in complex networks , 2009, 0907.1313.

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

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

[34]  P. Van Mieghem,et al.  Susceptible-infected-susceptible model: a comparison of N-intertwined and heterogeneous mean-field approximations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Matteo Magnani,et al.  Multidimensional epidemic thresholds in diffusion processes over interdependent networks , 2014, ArXiv.

[36]  Dawei Zhao,et al.  Immunization of Epidemics in Multiplex Networks , 2014, PloS one.

[37]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.