Metapopulation models for infectious diseases with applications to the Copenhagen cholera epidemic

Specialeforsvar ved Anne Lyngholm Sørensen

Titel: Metapopulation models for infectious diseases with applications to the Copenhagen cholera epidemic 

Abstract: Mathematical modelling of infectious diseases is about describing the transition of individuals between mutually exclusive infection states. In an analysis of the spread of an infectious disease the transition from the susceptible state to the infected state is the most important transition and the focus of modelling. The data of infectious diseases are of a non-experimental observation nature. This means that the statistical framework for the testing of a specific hypothesis is usually motivated by the character-ristics of the infectious disease, the population at risk and the geographical situation. This thesis is about the statistical modelling of the cholera epidemic in Copenhagen in 1853. To understand the transitions from susceptible to infected we develop a metapopulation framework. The models are based on a general SIR (Susceptible-Infected-Removed) model, which dynamics are described in a counting process frame-work. The metapopulations considered are based on a set of distinct quarters in Copenhagen in 1853. The models aim to distinct the transmission of cholera within the quarters from possible interactions with other quarters. The structure of interaction is based on quarters sharing a border and the direction of the water flow within the city. The data available for the statistical inference are weekly counts of newly infected on quarter level during the 15 weeks of the epidemic. We introduce internal and external auto-regressive covariates. In this we added a temporal dimension to the models. We focus on models in which we can test the effect of water contamination. In a first simple model we describe the transmission of cholera within the quarters by a single parameter which we assume to be the same for all quarters. We also describe the effect of transmission of cholera between quarters sharing a border by a single para-meter in order to estimate the effect of water contamination. The effect of water contamination is also described by a single parameter. The model was fitted as both an additive and multiplicative model. The simple model, when fitted to the data by maximum likelihood estimation, results in both a positive and negative effect of water contamination depending on whether it was fitted as an additive or a multiplicative model. This can be interpreted as to indicate that water contamination was not present. However, based on further analyses where we compared the simple model to more flexible models by means of goodness-of-fit statistics, it seems that the a more flexible model is preferred. For both of the more flexible models, the effect of water contamination was negative which also can be interpreted as to indicate that water contamination was not present. This thesis contributes with a extension of existing metapopulation models which can be used to test water effects. The final conclusion related to the Copenhagen cholera epidemic was that given the data, we were not able to properly test if water contamination was part of the Copenhagen cholera epidemic.

Vejledere: Susanne Ditlevsen, Thomas Alexander Gerds, Institut for Folkesundhed
Censor:     Ulrich Halekoh, SDU