Accounting for uncertainty in model-based prevalence estimation: paratuberculosis control in dairy herds (original) (raw)
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Theoretical Population Biology, 2010
Three different estimators are presented for the types of parameters present in mathematical models of animal epidemics. The estimators make use of data collected during an epidemic, which may be limited, incomplete, or under collection on an ongoing basis. When data are being collected on an ongoing basis, the estimated parameters can be used to evaluate putative control strategies. These estimators were tested using simulated epidemics based on a spatial, discrete-time, gravity-type, stochastic mathematical model containing two parameters. Target epidemics were simulated with the model and the three estimators were implemented using various combinations of collected data to independently determine the two parameters.
Mathematical modelling and prediction in infectious disease epidemiology
Clinical Microbiology and Infection, 2013
We discuss to what extent disease transmission models provide reliable predictions. The concept of prediction is delineated as it is understood by modellers, and illustrated by some classic and recent examples. A precondition for a model to provide valid predictions is that the assumptions underlying it correspond to the reality, but such correspondence is always limited-all models are simplifications of reality. A central tenet of the modelling enterprise is what we may call the 'robustness thesis': a model whose assumptions approximately correspond to reality will make predictions that are approximately valid. To examine which of the predictions made by a model are trustworthy, it is essential to examine the outcomes of different models. Thus, if a highly simplified model makes a prediction, and if the same or a very similar prediction is made by a more elaborate model that includes some mechanisms or details that the first model did not, then we gain some confidence that the prediction is robust. An important benefit derived from mathematical modelling activity is that it demands transparency and accuracy regarding our assumptions, thus enabling us to test our understanding of the disease epidemiology by comparing model results and observed patterns. Models can also assist in decision-making by making projections regarding important issues such as intervention-induced changes in the spread of disease.
Epidemics, 2014
Mathematical modeling of disease transmission has provided quantitative predictions for health policy, facilitating the evaluation of epidemiological outcomes and the cost-effectiveness of interventions. However, typical sensitivity analyses of deterministic dynamic infectious disease models focus on model architecture and the relative importance of parameters but neglect parameter uncertainty when reporting model predictions. Consequently, model results that identify point estimates of intervention levels necessary to terminate transmission yield limited insight into the probability of success. We apply probabilistic uncertainty analysis to a dynamic model of influenza transmission and assess global uncertainty in outcome. We illustrate that when parameter uncertainty is not incorporated into outcome estimates, levels of vaccination and treatment predicted to prevent an influenza epidemic will only have an approximately 50% chance of terminating transmission and that sensitivity analysis alone is not sufficient to obtain this information. We demonstrate that accounting for parameter uncertainty yields probabilities of epidemiological outcomes based on the degree to which data support the range of model predictions. Unlike typical sensitivity analyses of dynamic models that only address variation in parameters, the probabilistic uncertainty analysis described here enables modelers to convey the robustness of their predictions to policy makers, extending the power of epidemiological modeling to improve public health.
Use of Mathematical Models in Epidemiology to Predict Infectious
Partners Universal Multidisciplinary Research Journal (PUMRJ), 2024
Mathematical models play a key role in epidemiology, providing a powerful tool for predicting and controlling the spread of infectious diseases. This paper examines the use of mathematical models to analyze the dynamics of infectious diseases, assess the impact of health interventions, and predict future outbreaks. Initially, the structure of basic models such as SIR (Susceptible, Infected, Recovered) and their modifications to take into account factors such as population heterogeneity, social networks, and seasonal changes will be discussed. Next, model parameterization and calibration techniques will be explored to ensure accurate predictions in the context of data collected in real-time. The results show that mathematical models can be a valuable tool for public health policies, helping to identify optimal strategies for the prevention and control of infectious diseases. In conclusion, this analysis highlights the importance of the continued development of epidemiological models for improving the response to future epidemics and pandemics.
Calibration of individual-based models to epidemiological data: A systematic review
PLOS Computational Biology, 2020
Individual-based models (IBMs) informing public health policy should be calibrated to data and provide estimates of uncertainty. Two main components of model-calibration methods are the parameter-search strategy and the goodness-of-fit (GOF) measure; many options exist for each of these. This review provides an overview of calibration methods used in IBMs modelling infectious disease spread. We identified articles on PubMed employing simulation-based methods to calibrate IBMs informing public health policy in HIV, tuberculosis, and malaria epidemiology published between 1 January 2013 and 31 December 2018. Articles were included if models stored individual-specific information, and calibration involved comparing model output to population-level targets. We extracted information on parameter-search strategies, GOF measures, and model validation. The PubMed search identified 653 candidate articles, of which 84 met the review criteria. Of the included articles, 40 (48%) combined a quantitative GOF measure with an algorithmic parameter-search strategyeither an optimisation algorithm (14/40) or a sampling algorithm (26/40). These 40 articles varied widely in their choices of parameter-search strategies and GOF measures. For the remaining 44 (52%) articles, the parameter-search strategy could either not be identified (32/44) or was described as an informal, non-reproducible method (12/44). Of these 44 articles, the majority (25/44) were unclear about the GOF measure used; of the rest, only five quantitatively evaluated GOF. Only a minority of the included articles, 14 (17%) provided a rationale for their choice of model-calibration method. Model validation was reported in 31 (37%) articles. Reporting on calibration methods is far from optimal in epidemiological modelling studies of HIV, malaria and TB transmission dynamics. The adoption of better documented, algorithmic calibration methods could improve both reproducibility and the quality of inference in model-based epidemiology. There is a need for research comparing the performance of calibration methods to inform decisions about the parameter-search strategies and GOF measures.
The use of modelling to evaluate and adapt strategies for animal disease control
Revue Scientifique et Technique de l'OIE
Disease is often associated with debilitating clinical signs, disorders or production losses in animals and/or humans, leading to severe socioeconomic repercussions. This explains the high priority that national health authorities and international organisations give to selecting control strategies for and the eradication of specific diseases. When a control strategy is selected and implemented, an effective method of evaluating its efficacy is through modelling. To illustrate the usefulness of models in evaluating control strategies, the authors describe several examples in detail, including three examples of classification and regression tree modelling to evaluate and improve the early detection of disease: West Nile fever in equids, bovine spongiform encephalopathy (BSE) and multifactorial diseases, such as colony collapse disorder (CCD) in the United States. Also examined are regression modelling to evaluate skin test practices and the efficacy of an awareness campaign for bovine tuberculosis (bTB); mechanistic modelling to monitor the progress of a control strategy for BSE; and statistical nationwide modelling to analyse the spatio-temporal dynamics of bTB and search for potential risk factors that could be used to target surveillance measures more effectively. In the accurate application of models, an interdisciplinary rather than a multidisciplinary approach is required, with the fewest assumptions possible.
Inference for Individual-Level Models of Infectious Diseases in Large Populations
Statistica Sinica, 2010
Individual Level Models (ILMs), a new class of models, are being applied to infectious epidemic data to aid in the understanding of the spatio-temporal dynamics of infectious diseases. These models are highly flexible and intuitive, and can be parameterised under a Bayesian framework via Markov chain Monte Carlo (MCMC) methods. Unfortunately, this parameterisation can be difficult to implement due to intense computational requirements when calculating the full posterior for large, or even moderately large, susceptible populations, or when missing data are present. Here we detail a methodology that can be used to estimate parameters for such large, and/or incomplete, data sets. This is done in the context of a study of the UK 2001 foot-and-mouth disease (FMD) epidemic.