A Network-based Analysis of the 1861 Hagelloch Measles Data

Biometrics

Volumn 68, Issue 3, 2012, Pages 755-765

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

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b ROBERT MORRIS UNIVERSITY   (United States)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Exponential family Random Graph Model; Hagelloch; Measles; Networks

Indexed keywords

BAYESIAN NETWORKS; EPIDEMIOLOGY; MARKOV PROCESSES; STOCHASTIC MODELS;

EPIDEMIC MODELING; EXPONENTIAL FAMILY; EXPONENTIAL FAMILY RANDOM GRAPH MODEL; HAGELLOCH; MEASLE; NETWORK; NETWORK MODELS; NETWORK-BASED ANALYSIS; RANDOM GRAPH MODELS; STOCHASTICS;

STOCHASTIC SYSTEMS;

DATA SET; DISEASE TRANSMISSION; EPIDEMIC; EPIDEMIOLOGY; GRAPHICAL METHOD; INFECTIOUS DISEASE; MARKOV CHAIN; MEASLES; MONTE CARLO ANALYSIS; NETWORK ANALYSIS; NUMERICAL MODEL; SOFTWARE; STOCHASTICITY;

BADEN-WURTTEMBERG; GERMANY; HAGELLOCH;

EID: 84866748157     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2012.01748.x     Document Type: Article

References (35)

1. Anderson, R. and May, R. (1991). Infectious Diseases of Humans. Oxford: Oxford University Press.
2. Andersson, H. (1998). Limit theorems for a random graph epidemic model. Annals of Applied Probability 8, 1331-1349.
3. Atkinson, W., Wolfe, S., and Hamborsky, J. (2011). Epidemiology and Prevention of Vaccine-Preventable Diseases, 12th edition. Washington DC: Centers for Disease Control and Prevention.
4. Ball, F., Mollison, D., and Scalia-Tomba, G. (1997). Epidemics with two levels of mixing. The Annals of Applied Probability 7, 46-89.
5. Becker, N. and Utev, S. (1998). The effect of community structure on the immunity coverage required to prevent epidemics. Mathematical Biosciences 147, 23-39.
6. Britton, T., Kypraios, T., and O'Neill, P. (2011). Inference for epidemics with three levels of mixing: Methodology and application to a measles outbreak. Scandinavian Journal of Statistics 38, 578-599.
7. Britton, T. and O'Neill, P. (2002). Bayesian inference for stochastic epidemics in populations with random social structure. Scandinavian Journal of Statistics 29, 375-390.
8. Cauchemez, S., Bhattarai, A., Marchbanks, T. L., Fagan, R. P., Ostroff, S., Ferguson, N. M., Swerdlow, D., and the Pennsylvania H1N1 working group, (2011). Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza. Proceedings of the National Academy of Sciences 108, 2825-2830.
9. Eames, K. T., Tilston, N. L., and Edmunds, W. J. (2011). The impact of school holidays on the social mixing patterns of school children. Epidemics 3, 103-108.
10. Erdos, P. and Rényi, A. (1959). On random graphs. Publicationes Mathematicae 6, 290-297.
11. Gilbert, E. (1959). Random graphs. The Annals of Mathematical Statistics 30, 1141-1144.
12. Gough, K. (1977). The estimation of latent and infectious periods. Biometrika 64, 559-565.
13. Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
14. Groendyke, C., Welch, D., and Hunter, D. R. (2011). Bayesian inference for contact networks given epidemic data. Scandinavian Journal of Statistics 38, 600-616.
15. Hall, R. and Becker, N. (2009). Preventing epidemics in a community of households. Epidemiology and Infection 117, 443-455.
16. Keeling, M. and Eames, K. (2005). Networks and epidemic models. Journal of the Royal Society Interface 2, 295-307.
17. Keeling, M. and Rohani, P. (2008). Modeling infectious diseases in humans and animals. Clinical Infectious Diseases 47, 864-866.
18. Keeling, M., Woolhouse, M., May, R., Davies, G., and Grenfell, B. (2002). Modelling vaccination strategies against foot-and-mouth disease. Nature 421, 136-142.
19. Kenah, E. (2011). Contact intervals, survival analysis of epidemic data, and estimation of R0. Biostatistics 12, 548-566.
20. Lawson, A. and Leimich, P. (2000). Approaches to the space-time modelling of infectious disease behaviour. IMA Journal of Mathematics Applied in Medicine and Biology 17, 1-13.
21. Meyers, L. (2007). Contact network epidemiology: Bond percolation applied to infectious disease prediction and control. Bulletin of the American Mathematical Society 44, 63-86.
22. Meyers, L., Pourbohloul, B., Newman, M., Skowronski, D., and Brunham, R. (2005). Network theory and SARS: Predicting outbreak diversity. Journal of Theoretical Biology 232, 71-81.
23. Neal, P. and Roberts, G. (2004). Statistical inference and model selection for the 1861 Hagelloch measles epidemic. Biostatistics 5, 249-261.
24. Neal, P. and Roberts, G. (2005). A case study in non-centering for data augmentation: Stochastic epidemics. Statistics and Computing 15, 315-327.
25. Oesterle, H. (1992). Statistiche Reanalyse einer Masernepidemie 1861 in Hagelloch. M.D.Thesis, Eberhard-Karls Universität, Tübingen.
26. Pfeilsticker, A. (1863). Beiträge zur Pathologie der Masern mit besonderer Berücksichtigung der statistischen Verhältnisse. M.D. Thesis, Eberhard-Karls Universität, Tübingen.
27. R Development Core Team (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.
28. Ray, J. and Marzouk, Y. (2008). A Bayesian method for inferring transmission chains in a partially observed epidemic. Proceedings of the Joint Statistical Meetings: Conference Held in Denver, Colorado, August 3-7, 2008. Denver, CO: American Statistical Association.
29. Read, J. and Keeling, M. (2003). Disease evolution on networks: the role of contact structure. Proceedings of the Royal Society of London. Series B: Biological Sciences 270, 699-708.
30. Richardson, S. and Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society. Series B (Methodological) 59, 731-792.
31. Wallinga, J., Edmunds, W., and Kretzschmar, M. (1999). Perspective: Human contact patterns and the spread of airborne infectious diseases. TRENDS in Microbiology 7, 372-377.
32. Wallinga, J. and Teunis, P. (2004). Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. American Journal of Epidemiology 160, 509-516.
33. Wasserman, S. and Faust, K. (1994). Social Network Analysis: Methods and Applications. New York, NY: Cambridge University Press.
34. Wasserman, S. and Pattison, P. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika 61, 401-425.
35. Welch, D., Bansal, S., and Hunter, D. R. (2011). Statistical inference to advance network models in epidemiology. Epidemics 3, 38-45.