Epidemic transmission on random mobile network with diverse infection periods

Abstract The heterogeneity of individual susceptibility and infectivity and time-varying topological structure are two realistic factors when we study epidemics on complex networks. Current research results have shown that the heterogeneity of individual susceptibility and infectivity can increase the epidemic threshold in a random mobile dynamical network with the same infection period. In this paper, we will focus on random mobile dynamical networks with diverse infection periods due to people’s different constitutions and external circumstances. Theoretical results indicate that the epidemic threshold of the random mobile network with diverse infection periods is larger than the counterpart with the same infection period. Moreover, the heterogeneity of individual susceptibility and infectivity can play a significant impact on disease transmission. In particular, the homogeneity of individuals will avail to the spreading of epidemics. Numerical examples verify further our theoretical results very well.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

[3]  A. Rinaldo,et al.  Modelling cholera epidemics: the role of waterways, human mobility and sanitation , 2012, Journal of The Royal Society Interface.

[4]  Xiang Li,et al.  Epidemic prevalence on random mobile dynamical networks: individual heterogeneity and correlation , 2010 .

[5]  Xiao Fan Wang,et al.  Complex Networks: Topology, Dynamics and Synchronization , 2002, Int. J. Bifurc. Chaos.

[6]  Michael Small,et al.  Dynamical behaviour of an epidemic on complex networks with population mobility , 2009 .

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

[8]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Kazuyuki Aihara,et al.  Safety-Information-Driven Human Mobility Patterns with Metapopulation Epidemic Dynamics , 2012, Scientific Reports.

[10]  Alessandro Margheri,et al.  Heterogeneity in susceptibility to infection can explain high reinfection rates. , 2009, Journal of Theoretical Biology.

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

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  Zhang Duan-Ming,et al.  Steady States in SIRS Epidemical Model of Mobile Individuals , 2006 .

[14]  Octavio Miramontes,et al.  Dynamical small-world behavior in an epidemical model of mobile individuals , 2002 .

[15]  V. Latora,et al.  Disease spreading in populations of moving agents , 2007, 0707.1673.

[16]  Elisabeta Vergu,et al.  Impact of the Infection Period Distribution on the Epidemic Spread in a Metapopulation Model , 2010, PloS one.

[17]  Zonghua Liu,et al.  Epidemic spreading in communities with mobile agents , 2009 .

[18]  Andrea Baronchelli,et al.  Contagion dynamics in time-varying metapopulation networks , 2012, ArXiv.

[19]  Choy Heng Lai,et al.  Epidemic spreading induced by diversity of agents' mobility. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  H. J. Herrmann,et al.  Scaling of the propagation of epidemics in a system of mobile agents , 2004 .

[21]  James M Hyman,et al.  Differential susceptibility and infectivity epidemic models. , 2005, Mathematical biosciences and engineering : MBE.

[22]  Damian Clancy,et al.  SIR epidemic models with general infectious period distribution , 2014 .

[23]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..