Predicting an Predicting an EpidemicEpidemic

A Quantitative Assessment of TSE A Quantitative Assessment of TSE Sampling Data to Predict Outbreak Sampling Data to Predict Outbreak

MagnitudeMagnitudeAspen ShacklefordAspen Shackleford

HONR299JHONR299J

Variant Creutzfeldt-Jakob Disease (vCJD)

Linked to BSE

Unknown number of individuals who may be infected

Iatrogenic contamination

The National CJD Research & Surveillance Unit. (2014). Variant Creutzfeldt-Jakob Disease current data (March 2014) [Data file]. Retrieved from http://www.cjd.ed.ac.uk/documents/worldfigs.pdf

How are outbreak predictions made?

Reporting

Statistical Models

Dealler & Kent, 1995 Age of onset of clinical BSE symptoms was

sampled

Results Decrease in peak age of onset

Led to further investigation of under-reporting

Dealler, S.F. & Kent, J.T. (1995). BSE: an update on the statistical evidence. British Food Journal, 97 (8), 3-18. http://docserver.ingentaconnect.com

Under-Reporting MAFF Requirements

2 visits by a veterinarian

Slaughter and send in tissue sample

Case denial Dealler and Kent Suspicion

Paul Brown’s predictions

Farmer Initiative

Paul Brown’s Prediction

Brown, Paul. (2004). Mad Cow Disease in cattle and human beings: Bovine spongiform encephalopathy provides a case study in how to manage risks while still learning facts. American Scientist, 92 (4), 334-341. http://www.jstor.org/stable/27858422

Under-Reporting MAFF Requirements

2 visits by a veterinarian

Slaughter and send in tissue sample

Case denial Dealler and Kent Suspicion

Paul Brown’s predictions

Farmer Initiative

Dealler and Kent Statistical Model

(1995) Based upon data collection year (i) and

bovine age (j)

Follows a Poisson Distribution

Predicts the expected number of deaths at age j in year i from 1984 to 2001

Reporting effect and parameters compensated for under-reporting

Poisson Distribution Requirements

Used to determine the frequency of an abnormal event

Graphical representation r-curve closer to

zero signifies a rare event

The Warring States Project. (2007, August 24). Statistics: The Poisson distribution. Retrieved from http://www.umass.edu/wsp/resources/poisson/index.html

Dealler and Kent Statistical Model

(1995) Based upon data collection year and bovine

age

Follows a Poisson Distribution

Predicts the expected number of deaths at age j in year i from 1984 to 2001

Reporting effect and parameters compensated for under-reporting

Results Model predictions

from 1984 through 2001 (solid line)

Actual reports from 1984 to 1993 (dotted line)

Under-reporting

Peak in 1994

Overlap

Dealler, S.F. & Kent, J.T. (1995). BSE: an update on the statistical evidence. British Food Journal, 97 (8), 3-18. http://docserver.ingentaconnect.com

Hagenaars et al., 2006

Scrapie Within-flock model

Sheep age

Genotypes: ARR (0.45), ARQ (0.5), VRQ (0.05)

Between-flock model

Model determines duration and magnitude of an outbreak

N - flock-size

n - geometric mean of the size distribution

c1 , c2 – constants

Hagenaars, T.J, Donnelly, C.A., & Ferguson, N.M. (2006). Epidemiological analysis of data for scrapie in Great Britain. Epidemiology and Infection, 134 (2), 359-367. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870388/

Within Flock Results Large case rate

Case rate less than 5 per year

Average number of cases: 2.8 per year

Hagenaars, T.J, Donnelly, C.A., & Ferguson, N.M. (2006). Epidemiological analysis of data for scrapie in Great Britain. Epidemiology and Infection, 134 (2), 359-367. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870388/

γ – the rate of recovery of affected farms

λ - the rate per capita that a farm becomes affected

t - time (in years)

at>0 - the number of sheep flocks that have experienced at least one BSE case since the starting year

Hagenaars, T.J, Donnelly, C.A., & Ferguson, N.M. (2006). Epidemiological analysis of data for scrapie in Great Britain. Epidemiology and Infection, 134 (2), 359-367. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870388/

Between Flock Results

Low basic reproduction rate

High basic reproduction rate

Breeding for resistance ARR/ARR genotype

Changes in management

Hagenaars, T.J, Donnelly, C.A., & Ferguson, N.M. (2006). Epidemiological analysis of data for scrapie in Great Britain. Epidemiology and Infection, 134 (2), 359-367. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870388/

Conclusion Statistical models are widely used

Statistical models offer information that uses parameters and constraints that model real life

The predictions of statistical models can be used to make decisions about how to best prevent an outbreak that threatens human and animal populations