Bayesian Inference for Contact Networks Given Epidemic Data

Scandinavian Journal of Statistics

Volumn 38, Issue 3, 2011, Pages 600-616

  Groendyke, Chris ^a   Welch, David ^a   Hunter, David R ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Erdos R nyi; Exponential random graph model (ERGM); MCMC; Measles; Stochastic SEIR epidemic

Indexed keywords

EID: 79959651471     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2010.00721.x     Document Type: Article

References (27)

1. Anderson, R. & May, R. (1982). Directly transmitted infections diseases: control by vaccination. Science 215, 1053-1060.
2. Bailey, N. (1950). A simple stochastic epidemic. Biometrika 37, 193-202.
3. Barthelemy, M., Barrat, A., Pastor-Satorras, R. & Vespignani, A. (2005). Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. J. Theor. Biol. 235, 275-288.
4. Britton, T., Kypraios, T. & O'Neill, P. D. (2010). Inference for epidemics with three levels of mixing: methodology and application to a measles outbreak. Submitted.
5. Britton, T. & O'Neill, P. (2002). Bayesian inference for stochastic epidemics in populations with random social structure. Scand. J. Statist. 29, 375-390.
6. Edmunds, W., Gay, N., Kretzschmar, M., Pebody, R. & Wachmann, H. (2001). The pre-vaccination epidemiology of measles mumps and rubella in Europe: implications for modelling studies. Epidemiol. Infect. 125, 635-650.
7. Ferrari, M. (2006). Mixing models and the geometry of epidemics, PhD thesis. Pennsylvania State University, PA.
8. Gough, K. (1977). The estimation of latent and infectious periods. Biometrika 64, 559-565.
9. Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M., Morris, M. & Krivitsky, P. (2010). ergm: a package to fit simulate and diagnose exponential-family models for networks, version 2.2-3. Seattle, WA. Available on (accessed October 28, 2010).
10. 0. Math. Biosci. 215, 84-104.
11. Hunter, D. R., Goodreau, S. M. & Handcock, M. S. (2008a). Goodness of fit for social network models. J. Amer. Statist. Assoc. 103, 248-258.
12. Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M. & Morris, M. (2008b). ergm: a package to fit simulate and diagnose exponential-family models for networks. J. Stat. Softw. 24, 1-29.
13. Keeling, M. & Eames, K. (2005). Networks and epidemic models. J. Roy. Soc. Interface 2, 295-307.
14. Keeling, M. & Rohani, P. (2008). Modeling infectious diseases in humans and animals. Clin. Infect. Dis. 47, 864-866.
15. 0. Arxiv preprint arXiv:0912.3330.
16. Kermack, W. & McKendrick, A. (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 115, 700-721.
17. Meyers, L., Pourbohloul, B., Newman, M., Skowronski, D. & Brunham, R. (2005). Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232, 71-81.
18. Neal, P. & Roberts, G. (2004). Statistical inference and model selection for the 1861 Hagelloch measles epidemic. Biostatistics 5, 249-261.
19. Neal, P. & Roberts, G. (2005). A case study in non-centering for data augmentation: stochastic epidemics. Statist. Comput. 15, 315-327.
20. Oesterle, H. (1992). Statistiche Reanalyse einer Masernepidemiie 1861 in Hagelloch, MD thesis, Eberhard-Karls Universität, Tübingen.
21. Pfeilsticker, A. (1863). Beiträge zur Pathologie der Masern mit besonderer Berücksichtigung der statistischen Verhältnisse, MD thesis. Eberhard-Karls Universität, Tübingen.
22. R Development Core Team (2010). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; ISBN 3-900051-07-0.
23. Rahmandad, H. & Sterman, J. (2008). Heterogeneity and network structure in the dynamics of diffusion: comparing agent-based and differential equation models. Manage. Sci. 54, 998-1014.
24. Ray, J. & Marzouk, Y. (2008). A Bayesian method for inferring transmission chains in a partially observed epidemic. In Proceedings of the Joint Statistical Meetings: Conference Held in Denver, Colorado, 3-7 August 2008. American Statistical Association, Alexandria, VA, USA.
25. Schenzle, D. (1984). An age-structured model of pre- and post-vaccination measles transmission. Math. Med. Biol. 1, 169-191.
26. Snijders, T. A. B. (2002). Markov chain Monte Carlo estimation of exponential random graph models. J. Soc. Struct. 3, 1-40.
27. Volz, E. (2008). SIR dynamics in random networks with heterogeneous connectivity. J. Math. Biol. 56, 293-310.