Simulations of infectious diseases on networks

This paper examines the spread of diseases within populations in the context of networks of potentially disease-causing contacts. We examine the assumptions underlying classical mathematical models of epidemics and how more realistic assumptions can be made using contact networks. Several well-known kinds of contact networks are examined and simulated by evaluating their structural properties relevant to disease propagation. Algorithms used in the study of these networks are explained and numerical simulations of percolation and the epidemic process carried out to explore the effects that the network structure has on disease progression.

[1]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[2]  M M Telo da Gama,et al.  Recurrent epidemics in small world networks. , 2004, Journal of theoretical biology.

[3]  Jon M. Kleinberg,et al.  Navigation in a small world , 2000, Nature.

[4]  L. Sander,et al.  Geography in a scale-free network model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Mark Newman,et al.  Models of the Small World , 2000 .

[6]  Bryan Grenfell,et al.  Sexually transmitted diseases: Epidemic cycling and immunity , 2005, Nature.

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

[8]  P. Grassberger.  On the critical behavior of the general epidemic process and dynamical percolation , 1983 .

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

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

[11]  Christos Gkantsidis,et al.  The Markov Chain Simulation Method for Generating Connected Power Law Random Graphs , 2003, ALENEX.

[12]  M. Newman,et al.  Fast Monte Carlo algorithm for site or bond percolation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

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