Search

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1.

We consider the recently introduced edge-based compartmental models (EBCM) for the spread of susceptible-infected-recovered (SIR) diseases in networks. These models differ from standard infectious disease models by focusing on the status of a random partner in the population, rather than a random individual. This change in focus leads to simple analytic models for the spread of SIR diseases in random networks with heterogeneous degree. In this paper we extend this approach to handle deviations of the disease or population from the simplistic assumptions of earlier work. We allow the population to have structure due to effects such as demographic features or multiple types of risk behavior. We allow the disease to have more complicated natural history. Although we introduce these modifications in the static network context, it is straightforward to incorporate them into dynamic network models. We also consider serosorting, which requires using dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here. Our goal is twofold: to provide a number of examples generalizing the EBCM method for various different population or disease structures and to provide insight into how to derive such a model under new sets of assumptions.

BackgroundRecent focus on earlier detection of pathogen introduction in human and animal populations has led to the development of surveillance systems based on automated monitoring of health data. Real- or near real-time monitoring of pre-diagnostic data requires automated classification of records into syndromes--syndromic surveillance--using algorithms that incorporate medical knowledge in a reliable and efficient way, while remaining comprehensible to end users.MethodsThis paper describes the application of two of machine learning (Naïve Bayes and Decision Trees) and rule-based methods to extract syndromic information from laboratory test requests submitted to a veterinary diagnostic laboratory.ResultsHigh performance (F1-macro = 0.9995) was achieved through the use of a rule-based syndrome classifier, based on rule induction followed by manual modification during the construction phase, which also resulted in clear interpretability of the resulting classification process. An unmodified rule induction algorithm achieved an F(1-micro) score of 0.979 though this fell to 0.677 when performance for individual classes was averaged in an unweighted manner (F(1-macro)), due to the fact that the algorithm failed to learn 3 of the 16 classes from the training set. Decision Trees showed equal interpretability to the rule-based approaches, but achieved an F(1-micro) score of 0.923 (falling to 0.311 when classes are given equal weight). A Naïve Bayes classifier learned all classes and achieved high performance (F(1-micro)= 0.994 and F(1-macro) = .955), however the classification process is not transparent to the domain experts.ConclusionThe use of a manually customised rule set allowed for the development of a system for classification of laboratory tests into syndromic groups with very high performance, and high interpretability by the domain experts. Further research is required to develop internal validation rules in order to establish automated methods to update model rules without user input.