Large-scale properties of clustered networks: implications for disease dynamics

We consider previously proposed procedures for generating clustered networks and investigate how these procedures lead to differences in network properties other than clustering. We interpret our findings in terms of the effect of the network structure on the disease outbreak threshold and disease dynamics. To generate null-model networks for comparison, we implement an assortativity-conserving rewiring algorithm that alters the level of clustering while causing minimal impact on other properties. We show that many theoretical network models used to generate networks with a particular property often lead to significant changes in network properties other than that of interest. For high levels of clustering, different procedures lead to networks that differ in degree heterogeneity and assortativity, and in broader scale measures such as ℛ0 and the distribution of shortest path lengths. Hence, care must be taken when investigating the implications of network properties for disease transmission or other dynamic process that the network supports.

[1]  M. Serrano,et al.  Percolation and epidemic thresholds in clustered networks. , 2006, Physical review letters.

[2]  M E J Newman,et al.  Random graphs with clustering. , 2009, Physical review letters.

[3]  Darren M Green,et al.  Comment on "properties of highly clustered networks". , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Vázquez,et al.  Network clustering coefficient without degree-correlation biases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Andreas N. Lagerås,et al.  Epidemics on Random Graphs with Tunable Clustering , 2007, Journal of Applied Probability.

[6]  Istvan Z Kiss,et al.  Parameterization of individual-based models: comparisons with deterministic mean-field models. , 2006, Journal of theoretical biology.

[7]  I. Kiss,et al.  Disease contact tracing in random and clustered networks , 2005, Proceedings of the Royal Society B: Biological Sciences.

[8]  P. Trapman,et al.  On analytical approaches to epidemics on networks. , 2007, Theoretical population biology.

[9]  Marián Boguñá,et al.  Clustering in complex networks. II. Percolation properties. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  R R WILLCOX,et al.  Treatment of Early Syphilis with Penicillin, Neoarsphenamine, and Bismuth , 1948, The British journal of venereal diseases.

[11]  K. Eames,et al.  Modelling disease spread through random and regular contacts in clustered populations. , 2008, Theoretical population biology.

[12]  Håkan Andersson,et al.  Limit theorems for a random graph epidemic model , 1998 .

[13]  M. Newman.  Properties of highly clustered networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[15]  L. Danon,et al.  Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain , 2006, Proceedings of the Royal Society B: Biological Sciences.

[16]  A. Ghani,et al.  The Role of Sexual Partnership Networks in the Epidemiology of Gonorrhea , 1997, Sexually transmitted diseases.

[17]  Matt J Keeling,et al.  Contact tracing and disease control , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[18]  Matt J. Keeling,et al.  The Impact of Contact Tracing in Clustered Populations , 2010, PLoS Comput. Biol..

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

[20]  Mark D. F. Shirley,et al.  The impacts of network topology on disease spread , 2005 .

[21]  R. May,et al.  Networks of sexual contacts: implications for the pattern of spread of HIV , 1989, AIDS.

[22]  M. Keeling,et al.  The effects of local spatial structure on epidemiological invasions , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[23]  J. Robins,et al.  Second look at the spread of epidemics on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Joel C. Miller.  Spread of infectious disease through clustered populations , 2008, Journal of The Royal Society Interface.

[25]  Darren Michael Green,et al.  Small- and large-scale network structure of live fish movements in Scotland. , 2009, Preventive veterinary medicine.

[26]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[27]  James M Robins,et al.  Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing. , 2007, Journal of theoretical biology.

[28]  János Kertész,et al.  Clustering in complex networks , 2004 .

[29]  Joel E. Cohen,et al.  Infectious Diseases of Humans: Dynamics and Control , 1992 .

[30]  M. Keeling,et al.  Disease evolution on networks: the role of contact structure , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[31]  B T Grenfell,et al.  Individual-based perspectives on R(0). , 2000, Journal of theoretical biology.

[32]  J M Hyman,et al.  Risk behavior-based model of the cubic growth of acquired immunodeficiency syndrome in the United States. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[33]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[34]  R. Anderson,et al.  Mathematical Models of the Transmission and Control of Sexually Transmitted Diseases , 2000, Sexually transmitted diseases.

[35]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[36]  Joel C. Miller,et al.  Percolation and epidemics in random clustered networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Joel C. Miller,et al.  Epidemic size and probability in populations with heterogeneous infectivity and susceptibility. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[40]  Shashank Khandelwal,et al.  Exploring biological network structure with clustered random networks , 2009, BMC Bioinformatics.

[41]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  R. Kao.  Evolution of pathogens towards low R0 in heterogeneous populations , 2006, Journal of theoretical biology.

[43]  S. Gupta,et al.  The significance of sexual partner contact networks for the transmission dynamics of HIV. , 1990, Journal of acquired immune deficiency syndromes.

[44]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Reuven Cohen,et al.  Percolation critical exponents in scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Gábor Csányi,et al.  Polynomial epidemics and clustering in contact networks , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[47]  I. Kiss,et al.  The effect of network mixing patterns on epidemic dynamics and the efficacy of disease contact tracing , 2007, Journal of The Royal Society Interface.

[48]  Rowland R Kao,et al.  The effect of contact heterogeneity and multiple routes of transmission on final epidemic size. , 2006, Mathematical biosciences.