@PHDTHESIS\{IMM2004-03361,
    author       = "L. E. Christiansen",
    title        = "Nonlinear time series analysis of zoonoses",
    year         = "2004",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by prof. Henrik Madsen, {IMM}.",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/3361-full.html",
    abstract     = "The present thesis consists of a summary report and four research papers. The subject of the thesis is temporal and spatial correlations in epidemiologic data. 

The summary report consists of three parts. The first part is an application of locally weighted least squares, the second part suggests expansions of the spatial scan statistic, and the third part is on modelling using stochastic di erential equations.

The first part is related to Paper B and the problem was how climatic variables predict Campylobacter in broiler  ocks and humans. The problem was targeted using locally weighted least squares with zero to second order polynomials; cross validation was used to avoid over tting the data. It was found that temperature is a good predictor for Campylobacter infections. For broiler  ocks the highest proportion of positive  ocks was seen in weeks with sustained high temperatures throughout a week, for humans warm days and more sunshine resulted in the highest incidence. The dependence was non-linear and the lag between high temperature and registred infection was 3 to 4 weeks. The ambient temperature is believed to drive something else that can transfer infections to broiler flocks.

The second part is related to Paper C and the question was if there was spatial clustering of the proportion of positive broiler flocks. The spatial scan statistic is able to both locate and test for signi cance of a cluster, the problem with the method is that previously only circular clusters were allowed. This work presents an algorithm for creation of the set of confocal ellipses which is a natural expansion of the set of concentric circles previously used. A new way of presenting the set of clusters is also presented. Clustering was found to occur; Funen and the nearest part of Jutland is a low risk region whereas the Northwest part of Jutland is a high risk region for Campylobacter infected broiler flocks.

The third part is related to Paper D and E and the problem was to make a model for growth in a rich media including the dependence on the concentration of copper in the media. Bacterial growth involves many processes within the cells and it is shown why the continuous-discrete stochastic state space models have an advantage over the often used ordinary di erential equations. The parameters of five candidate models have been estimated using data for one concentration of copper. With the given dataset the simpler models performed better than the more complicated models. It was chosen to implement two simple copper dependencies in three of the models. In all three models the multiplicative approach was better than the additive approach.

In all three parts suggestions for further work have been proposed."
}