Model

Illnesses like infections, cold, influenza and so on in type 1 diabetes mellitus (T1DM) patients, can compromise the daily patient administered diabetes treatment. This in turn may result in fluctuating blood glucose concentrations, especially hyperglycemia for prolonged periods, which over time can cause serious late complications. The illness prediction project at Tromsø Telemedicine Laboratory aims to construct a prediction model that, through use of patient observable parameters, for example, blood glucose, insulin injections and body temperature, can significantly identify risk of developing illnesses, before onset of symptoms and before illness onset.

Such a model could potentially enable T1DM patients to fight the illnesses, and prepare for an adequate change in the T1DM-management earlier on.

Objective

To develop an illness prediction model that can predict illness in T1DM patients before onset of symptoms, using the patient’s observable parameters.

The evolution of a communicable disease in a human population is not entirely predictable. However, the spreading process can be assumed to vary smoothly in time. The time-dependent infection process can be linked to observations of the epidemic’s evolution by convolving it with a stochastic delay model. In retrospective analyses of epidemics, when the observations are the dates of exhibition of patients’ symptoms, the delay is the incubation period. In case of biosurveillance data, the delay is caused by incubation and a (hospital) visit delay, modeled as independent random variables. A model for observational error is also required. The time-dependent infection/spread rate may be inferred from observations by a deconvolution process. The smooth temporal variation of the infection rate allows its representation using a low dimensional parametric model, and the inference may be performed with relatively little data. For large outbreaks, the data may be available early in the epidemic, allowing timely modeling of the outbreak. Short-term forecasts using the model could thereafter be used for medical planning.

Objective

We present a statistical method to characterize an epidemic of a communicable disease from a time series of patients exhibiting symptoms. Characterization is defined as estimating an unobserved, time-dependent infection rate and associated parameters that completely define the evolution of an epidemic. The problem is posed as one of Bayesian inference, where parameters are inferred with quantified uncertainty. The method is demonstrated on synthetic and historical epidemic data.