An epidemic model on evolving networks

The evolving networks are extensive in many real world networks, which are characterized by rearrangements of the links between nodes. In this paper we develop an SEIRS epidemic models on evolving networks using a general ordinary differential equation (ODE) model, and further the basic reproduction number is obtained. The basic reproduction number in epidemic systems is the critical condition which determines the spread of the disease. The analysis of the evolving SEIRS networks show that different rewiring process can get different thresholds of system.

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

[2]  N. Konno,et al.  Multi-state epidemic processes on complex networks. , 2005, Journal of theoretical biology.

[3]  Junling Ma,et al.  Network evolution by different rewiring schemes , 2009 .

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

[5]  Gueorgi Kossinets,et al.  Empirical Analysis of an Evolving Social Network , 2006, Science.

[6]  Xianmin Geng,et al.  Random models of scale-free networks , 2005 .

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

[8]  Tao Zhou,et al.  Epidemic spreading on heterogeneous networks with identical infectivity , 2007 .

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

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

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

[12]  A. Barabasi,et al.  Quantifying social group evolution , 2007, Nature.

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

[14]  Zhidong Teng,et al.  On a Nonautonomous SEIRS Model in Epidemiology , 2007, Bulletin of mathematical biology.

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

[16]  Jie Lou,et al.  The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network , 2010 .

[17]  Jin Zhen,et al.  Cellular automata modelling of SEIRS , 2005 .

[18]  Guanrong Chen,et al.  Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.