**Published on** February 19th, 2014 |
*by Emily Corbett*

# Epidemiological studies

By Brock Hermans, University of Adelaide

*This student took part in the 2012/13 AMSI Vacation Research Scholarship program. For more information on this years program please click here*

In many epidemiological studies one of the key questions we want to ask is, what is the infectivity rate of a particular disease? That is, at what rate do people become infected by a disease. Knowing such information can help us to implement strategies in order to prevent a disease from spreading through a population. My research project focused on laying the foundations for estimating infectivity rates in a population where contact between individuals is unknown. What we do is take a method known as approximate Bayesian computation (ABC) which estimates parameters and then use the SEIR model to estimate the transition rates for a disease.

The idea behind ABC is that if there is some parameter that we want to estimate and we have some data that we observed, then we should simulate a value for the parameter, use that value to generate some artificial data and then compare the observed data to the artificial data (we will go into how we do this comparison of the data later). If they are similar then the value we simulated for the parameter could be a good estimate for the true parameter. We then continue this simulation and comparison multiple times and get a series of estimates for the parameter.

So what we want to be able to do is use the ABC algorithm to estimate parameters of the SEIR model. The SEIR model is a continuous-time model that describes how a disease can move through a population of people. It follows the idea that a disease has certain stages and it groups people into categories based on what stage a person is in; you start off not having the disease (susceptible), then you are exposed to it and will develop it but do not yet show symptoms (exposed), then you are infectious to others (infective) and then you recover (recovered). As such, the SEIR model splits the population into four categories, (S)usceptible, (E)xposed, (I)nfective and (R)ecovered. An individual can be in one group only at a time, and they can either stay in their current group or move to the next stage, with the exception being the recovered group whose must stay in the recovered group once in there. This constraint on the recovered group movement is based on a disease with immunity.

There are three parameters that govern the rate at which an individual moves along to the next group. We want to be able to apply ABC to the SEIR model in order to determine these three parameters, however we were unable to find a way to compare the observed data to the artificial data. This comparison step we mentioned before is done through summary statistics, which summarise our data for us, ideally without losing any information. Having tried several different methods of summary statistic selection we were unable to find one that worked consistently for the SEIR model.

In the project we examined some basic Bayesian statistics, the ABC algorithm, some recent developments in ABC and the SEIR model. We were unsuccessful in being able to apply our ABC algorithm to the SEIR model, however continued research into this area should focus on different ways of choosing appropriate summary statistics. Once this is done, we can then take some real world data and estimate the transition rates of the SEIR model.

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