Open Access Research article

Accounting for uncertainty in model-based prevalence estimation: paratuberculosis control in dairy herds

Ross S Davidson1*, Iain J McKendrick2, Joanna C Wood2, Glenn Marion2, Alistair Greig1, Karen Stevenson3, Michael Sharp4 and Michael R Hutchings1

Author Affiliations

1 Disease Systems, SAC, , West Mains Road, Edinburgh EH9 3JG, UK

2 , Biomathematics & Statistics Scotland, JCMB, The King’s Buildings, Edinburgh EH9 3JZ, UK

3 , Moredun Research Institute, Bush Loan, Penicuik EH26 0PZ, UK

4 , Veterinary Laboratories Agency, Lasswade, Bush Loan, Penicuik EH26 0PZ, UK

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BMC Veterinary Research 2012, 8:159  doi:10.1186/1746-6148-8-159

Published: 10 September 2012



A common approach to the application of epidemiological models is to determine a single (point estimate) parameterisation using the information available in the literature. However, in many cases there is considerable uncertainty about parameter values, reflecting both the incomplete nature of current knowledge and natural variation, for example between farms. Furthermore model outcomes may be highly sensitive to different parameter values. Paratuberculosis is an infection for which many of the key parameter values are poorly understood and highly variable, and for such infections there is a need to develop and apply statistical techniques which make maximal use of available data.


A technique based on Latin hypercube sampling combined with a novel reweighting method was developed which enables parameter uncertainty and variability to be incorporated into a model-based framework for estimation of prevalence. The method was evaluated by applying it to a simulation of paratuberculosis in dairy herds which combines a continuous time stochastic algorithm with model features such as within herd variability in disease development and shedding, which have not been previously explored in paratuberculosis models. Generated sample parameter combinations were assigned a weight, determined by quantifying the model’s resultant ability to reproduce prevalence data. Once these weights are generated the model can be used to evaluate other scenarios such as control options. To illustrate the utility of this approach these reweighted model outputs were used to compare standard test and cull control strategies both individually and in combination with simple husbandry practices that aim to reduce infection rates.


The technique developed has been shown to be applicable to a complex model incorporating realistic control options. For models where parameters are not well known or subject to significant variability, the reweighting scheme allowed estimated distributions of parameter values to be combined with additional sources of information, such as that available from prevalence distributions, resulting in outputs which implicitly handle variation and uncertainty. This methodology allows for more robust predictions from modelling approaches by allowing for parameter uncertainty and combining different sources of information, and is thus expected to be useful in application to a large number of disease systems.