Infection Dynamics on Growing Networks

We consider the entire spectrum of architectures for large, growing, and complex networks, ranging from being heterogeneous (scale-free) to homogeneous (random or small-world), and investigate the infection dynamics by using a realistic three-state epidemiological model. In this framework, a node can be in one of the three states: susceptible (S), infected (I), or refractory (R), and the populations in the three groups are approximately described by a set of nonlinear differential equations. Our heuristic analysis predicts that, (1) regardless of the network architecture, there exists a substantial fraction of nodes that can never be infected, and (2) heterogeneous networks are relatively more robust against spread of infection as compared with homogeneous networks. These are confirmed numerically. We have also considered the problem of deliberate immunization for preventing wide spread of infection, with the result that targeted immunization can be quite effective for heterogeneous networks. We believe these results are important for a host of problems in many areas of natural science and engineering, and in social sciences as well.

[1]  Roy M. Anderson,et al.  The Transmission Dynamics of Human Immunodeficiency Virus (HIV) , 1988 .

[2]  S Redner,et al.  Degree distributions of growing networks. , 2001, Physical review letters.

[3]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.

[4]  B. Tadić.  Dynamics of directed graphs: the world-wide Web , 2000, cond-mat/0011442.

[5]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

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

[7]  A. Sudbury.  The proportion of the population never hearing a rumour , 1985 .

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

[9]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[10]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[11]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  S. Redner,et al.  Organization of growing random networks. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[14]  Partha Dasgupta,et al.  Topology of the conceptual network of language. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Nong Ye,et al.  Statistical properties and attack tolerance of growing networks with algebraic preferential attachment. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

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