Epidemic spreading model of complex dynamical network with the heterogeneity of nodes

In this paper, we model epidemic spreading by considering the mobility of nodes in complex dynamical network based on mean field theory using differential equations. Moreover, a resistance factor which can characterise the impact of individual's difference on the propagation dynamics in complex dynamical network is proposed by considering the influence of total number of connections and the continuous time to remain in contact. The effect of heterogeneity on the evolution process of propagation dynamics is explored by simulation. Extensive simulations are conducted to study the key influence parameters and the influence of them on the spreading dynamics, which are helpful to the understanding of epidemic spreading mechanism and the designing of effective control strategies.

[1]  Jiajia Wang,et al.  SIRaRu rumor spreading model in complex networks , 2014 .

[2]  Sancheng Peng,et al.  Survivability modeling and analysis on 3D mobile ad-hoc networks , 2011 .

[3]  William Hugh Murray,et al.  The application of epidemiology to computer viruses , 1988, Comput. Secur..

[4]  Xinchu Fu,et al.  Spreading of epidemics on scale-free networks with nonlinear infectivity , 2009 .

[5]  Legand L. Burge,et al.  Modelling the spread of mobile malware , 2008, Int. J. Comput. Aided Eng. Technol..

[6]  David A. Maltz,et al.  A performance comparison of multi-hop wireless ad hoc network routing protocols , 1998, MobiCom '98.

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

[8]  Yan-Wu Wang,et al.  Synchronization of complex dynamical networks under recoverable attacks , 2010, Autom..

[9]  Bimal Kumar Mishra,et al.  Dynamic model of worm propagation in computer network , 2014 .

[10]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Suh-Yuh Yang,et al.  Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[12]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[13]  Bei Kang,et al.  Orientation accuracy analysis of multiple satellite networks using epidemic model , 2009, Int. J. Syst. Sci..

[14]  Yasuhiro Takeuchi,et al.  Global stability of an SIR epidemic model with time delays , 1995, Journal of mathematical biology.

[15]  Sancheng Peng,et al.  Modeling the dynamics of worm propagation using two-dimensional cellular automata in smartphones , 2013, J. Comput. Syst. Sci..

[16]  Maziar Nekovee,et al.  The Opportunistic Transmission of Wireless Worms between Mobile Devices , 2008, ArXiv.

[17]  Sancheng Peng,et al.  Modeling Malware Propagation in Smartphone Social Networks , 2013, 2013 12th IEEE International Conference on Trust, Security and Privacy in Computing and Communications.

[18]  Ju H. Park,et al.  Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling , 2012, Appl. Math. Comput..

[19]  David A. Maltz,et al.  Dynamic Source Routing in Ad Hoc Wireless Networks , 1994, Mobidata.

[20]  M. Li,et al.  Global dynamics of a SEIR model with varying total population size. , 1999, Mathematical Biosciences.

[21]  Xiang Li,et al.  On the stability of epidemic spreading in small-world networks: how prompt the recovery should be? , 2007, Int. J. Syst. Sci..

[22]  Ming Tang,et al.  Epidemic spreading on complex networks with general degree and weight distributions , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Zengqiang Chen,et al.  EPIDEMICS OF SIRS MODEL WITH NONUNIFORM TRANSMISSION ON SCALE-FREE NETWORKS , 2009 .

[24]  R Ross,et al.  SOME A PRIORI PATHOMETRIC EQUATIONS , 1915, British medical journal.

[25]  Min Wu,et al.  Propagation model of smartphone worms based on semi-Markov process and social relationship graph , 2014, Comput. Secur..

[26]  Tracy Camp,et al.  A survey of mobility models for ad hoc network research , 2002, Wirel. Commun. Mob. Comput..

[27]  Sancheng Peng,et al.  Worm Propagation Modeling Using 2D Cellular Automata in Bluetooth Networks , 2011, 2011IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications.

[28]  H. Hethcote.  Qualitative analyses of communicable disease models , 1976 .

[29]  Jiang Guoping,et al.  Epidemic spreading model and stability of the networks in mobile environment , 2012 .