no. 1
Numéro spécial : Special Issue on Modelling and Inference for Infectious diseases
The BSE epidemic in Great-Britain: a generic example of risk assessment during the growth and decay phases
[L’épidémie d’ESB en Grande-Bretagne : un exemple générique d’évaluation des risques au cours des phases de croissance et de déclin]
Journal de la société française de statistique, Tome 157 (2016) no. 1, pp. 101-128.

Dans cet article nous proposons une analyse complète de l’évolution de l’épidémie d’encéphalopathie spongiforme bovine en Grande-Bretagne. Notre étude est basée sur un modèle de processus de branchement multitype et sur différents outils probabilistes et statistiques. Nous nous focalisons en premier lieu sur la phase de croissance jusqu’à la première mesure de contrôle sanitaire en 1988, pour laquelle nous proposons une estimation des paramètres inconnus de notre modèle via une approche bayésienne. Nous considérons ensuite la phase de déclin et estimons par une approche fréquentiste le paramètre d’infection afférent, ce qui nous permet de prédire l’incidence des cas à venir, le temps d’extinction de l’épidémie ainsi que sa taille totale. Pour finir, nous évaluons les risques qui seraient conséquents à une très longue phase de déclin. Dans ce but nous conditionnons le processus à une extinction très tardive, et prédisons grâce à une estimation du paramètre d’infection l’évolution de l’épidémie dans le cas de ce scénario le plus défavorable.

In this paper we provide a comprehensive analysis of the Bovine spongiform encephalopathy (BSE) epidemic evolution in Great-Britain. Our study is based on a multi-type branching process model and on different stochastic and statistical tools. We first focus on the growth phase until the first sanitary control measure in 1988, and provide an estimation of the unknown parameters of our model, using a Bayesian approach. We then consider the decay phase of the epidemic and estimate its new infection parameter using a frequentist approach, which enables us to predict the future incidences of cases, the epidemic extinction time and the total epidemic size. We finally evaluate the risks that would be caused by a very long decay phase. For this purpose we condition the process on a very late extinction, and thanks to an estimation of the infection parameter, we predict the evolution of the epidemic in this worst-case scenario.

Keywords: stochastic epidemic, SEI, branching process, Q-process, worst-case scenario, Bayesian inference, CLSE, consistency and asymptotic normality
Mot clés : ESB, modèle épidémique stochastique, SEI, processus de branchement, Q-processus, pire scénario, inférence bayésienne, estimateur des moindres carrés conditionnels, consistance et normalité asymptotique 
@article{JSFS_2016__157_1_101_0,
     author = {Jacob, Christine and P\'enisson, Sophie},
     title = {The {BSE} epidemic in {Great-Britain:} a generic example of risk assessment during the growth and decay phases},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {101--128},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {157},
     number = {1},
     year = {2016},
     zbl = {1357.92072},
     language = {en},
     url = {http://www.numdam.org/item/JSFS_2016__157_1_101_0/}
}
TY  - JOUR
AU  - Jacob, Christine
AU  - Pénisson, Sophie
TI  - The BSE epidemic in Great-Britain: a generic example of risk assessment during the growth and decay phases
JO  - Journal de la société française de statistique
PY  - 2016
SP  - 101
EP  - 128
VL  - 157
IS  - 1
PB  - Société française de statistique
UR  - http://www.numdam.org/item/JSFS_2016__157_1_101_0/
LA  - en
ID  - JSFS_2016__157_1_101_0
ER  - 
%0 Journal Article
%A Jacob, Christine
%A Pénisson, Sophie
%T The BSE epidemic in Great-Britain: a generic example of risk assessment during the growth and decay phases
%J Journal de la société française de statistique
%D 2016
%P 101-128
%V 157
%N 1
%I Société française de statistique
%U http://www.numdam.org/item/JSFS_2016__157_1_101_0/
%G en
%F JSFS_2016__157_1_101_0
Jacob, Christine; Pénisson, Sophie. The BSE epidemic in Great-Britain: a generic example of risk assessment during the growth and decay phases. Journal de la société française de statistique, Tome 157 (2016) no. 1, pp. 101-128. http://www.numdam.org/item/JSFS_2016__157_1_101_0/

[1] Anderson, R. M.; Donnelly, C. A.; Ferguson, N. M.; Woolhouse, M. E. J.; Watt, C. J.; Udy, H. J.; MaWhinney, S.; Dunstan, S. P.; Southwood, T. R. E.; Wilesmith, J. W.; Ryan, J. B. M.; Hoinville, L. J.; Hillerton, J. E.; Austin, A. R.; Wells, G. A. H. Transmission dynamics and epidemiology of BSE in British cattle, Nature, Volume 382 (1996) no. 6594, pp. 779-788

[2] Arratia, R.; Goldstein, L.; Gordon, L. Two Moments Suffice for Poisson Approximations: The Chen-Stein Method., Ann. Probab., Volume 17 (1989) no. 1, pp. 9-25 | Zbl

[3] Athreya, K. B.; Ney, P. E. Branching processes, Springer-Verlag, New-York, 1972 | Zbl

[4] Consul, P. C.; Famoye, F. Lagrangian probability distributions, Birkhäuser Boston, Inc., Boston, MA, 2006 | Zbl

[5] Department for Environment, Food & Rural Affairs Cattle TSE surveillance statistics, http://www.defra.gov.uk/ahvla-en/publication/tse-stats-cattle/ , 2014 ([Online; accessed April-2015])

[6] Devroye, L. The branching process method in Lagrange random variate generation, Communications in Statistics-Simulation and Computation, Volume 21 (1992), pp. 1-14 | Zbl

[7] Dallaporta, S.; Joffe, A. The Q -process in a multitype branching process, International Journal of Pure and Applied Mathematics, Volume 42 (2008) no. 2, pp. 235-240 | Zbl

[8] Donnelly, C. A. Maternal transmission of BSE: interpretation of the data on the offspring of BSE-affected pedigree suckler cows, Veterinary Record, Volume 142 (1998) no. 21, pp. 579-580

[9] HMSO The Bovine Spongiform Encephalopathy Order, http://www.legislation.gov.uk/uksi/1996/2007/contents/made , 1996 no. 2007 ([Online; accessed April-2015])

[10] Harris, T. E. Branching processes, Annals of Mathematical Statistics, Volume 19 (1948) no. 4, pp. 474-494 | Zbl

[11] Jacob, C.; Maillard, L.; Denis, J. B.; Bidot, C. Stochastic modelling of the incidence of clinical cases of a rare fatal SEI disease in a large branching population structured in ages. Example of the BSE epidemic in Great-Britain. (2008) (Technical report)

[12] Jacob, C.; Maillard-Teyssier, L.; Denis, J. B.; Bidot, C. A branching process approach for the propagation of the bovine spongiform encephalopathy in Great Britain, Workshop on Branching Processes and Their Applications (González Velasco, M.; Puerto, I.M.; Martínez, R.; Molina, M.; Mota, M.; Ramos, A., eds.) (Lecture Notes in Statistics), Volume 197, Springer Berlin Heidelberg (2010), pp. 225-241

[13] Joffe, A.; Spitzer, F. On multitype branching processes with ρ ⩽ 1 , Journal of Mathematical Analysis and Application, Volume 19 (1967) no. 3, pp. 409-430 | Zbl

[14] OpenBUGS http://www.openbugs.net/ , 2009 ([Online; accessed April-2015])

[15] Pénisson, S. Estimation of the infection parameter of an epidemic modeled by a branching process, Electronic Journal of Statistics, Volume 8 (2014) no. 2 | Zbl

[16] Pénisson, S.; Jacob, C. Stochastic Methodology for the Study of an Epidemic Decay Phase, Based on a Branching Model, International Journal of Stochastic Analysis, Volume 2012 (2012) | Zbl

[17] Supervie, V.; Costagliola, D. The unrecognised French BSE epidemic, Veterinary Research, Volume 35 (2004) no. 3, pp. 349-362

[18] World Organisation for Animal Health Number of cases of bovine spongiform encephalopathy (BSE) reported in the United Kingdom, http://www.oie.int/en/animal-health-in-the-world/bse-specific-data/number-of-cases-in-the-united-kingdom/ , 2014 ([Online; accessed April-2015])

[19] Wells, G. A.; Scott, A. C.; Johnson, C. T.; Gunning, R. F.; Hancock, R. D.; Jeffrey, M.; Dawson, M.; Bradley, R. A novel progressive spongiform encephalopathy in cattle, Veterinary Record, Volume 121 (1987) no. 18, pp. 419-420