Is Network Clustering Detectable in Transmission Trees?

Networks are often used to model the contact processes that allow pathogens to spread between hosts but it remains unclear which models best describe these networks. One question is whether clustering in networks, roughly defined as the propensity for triangles to form, affects the dynamics of disease spread. We perform a simulation study to see if there is a signal in epidemic transmission trees of clustering. We simulate susceptible-exposed-infectious-removed (SEIR) epidemics (with no re-infection) over networks with fixed degree sequences but different levels of clustering and compare trees from networks with the same degree sequence and different clustering levels. We find that the variation of such trees simulated on networks with different levels of clustering is barely greater than those simulated on networks with the same level of clustering, suggesting that clustering can not be detected in transmission data when re-infection does not occur.

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

[2]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  A. Rambaut,et al.  Episodic Sexual Transmission of HIV Revealed by Molecular Phylodynamics , 2008, PLoS medicine.

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

[5]  Mathieu Moslonka-Lefebvre,et al.  Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering. , 2009, Journal of theoretical biology.

[6]  Edoardo M. Airoldi,et al.  A Survey of Statistical Network Models , 2009, Found. Trends Mach. Learn..

[7]  X ZhengAlice,et al.  A Survey of Statistical Network Models , 2010 .

[8]  J. Wallinga,et al.  Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures , 2004, American journal of epidemiology.

[9]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[10]  Martina Morris,et al.  Network Epidemiology: A Handbook for Survey Design and Data Collection , 2004 .

[11]  Gaël Thébaud,et al.  Integrating genetic and epidemiological data to determine transmission pathways of foot-and-mouth disease virus , 2008, Proceedings of the Royal Society B: Biological Sciences.

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

[13]  S. Harrison,et al.  Long-COVID Symptoms in Individuals Infected with Different SARS-CoV-2 Variants of Concern: A Systematic Review of the Literature , 2022, Viruses.

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

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

[16]  M. Kretzschmar,et al.  Using data on social contacts to estimate age-specific transmission parameters for respiratory-spread infectious agents. , 2006, American journal of epidemiology.

[17]  Jennifer Badham,et al.  The impact of network clustering and assortativity on epidemic behaviour. , 2010, Theoretical population biology.

[18]  David Welch,et al.  A Network‐based Analysis of the 1861 Hagelloch Measles Data , 2012, Biometrics.

[19]  Maria A. Kazandjieva,et al.  A high-resolution human contact network for infectious disease transmission , 2010, Proceedings of the National Academy of Sciences.

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

[21]  M. Steel,et al.  Distributions of cherries for two models of trees. , 2000, Mathematical biosciences.

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

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

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

[25]  P. O’Neill,et al.  Bayesian inference for stochastic epidemics in populations with random social structure , 2002 .

[26]  M. Keeling.  The implications of network structure for epidemic dynamics. , 2005, Theoretical population biology.

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

[28]  Andrew Rambaut,et al.  Evolutionary analysis of the dynamics of viral infectious disease , 2009, Nature Reviews Genetics.

[29]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[30]  R. Mikolajczyk,et al.  Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases , 2008, PLoS medicine.

[31]  Shweta Bansal,et al.  Statistical inference to advance network models in epidemiology. , 2011, Epidemics.

[32]  F. Ball,et al.  Analysis of a stochastic SIR epidemic on a random network incorporating household structure. , 2010, Mathematical biosciences.

[33]  D. Hunter,et al.  Bayesian Inference for Contact Networks Given Epidemic Data , 2010 .

[34]  P. Mucha,et al.  The unreasonable effectiveness of tree-based theory for networks with clustering. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[36]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.