Stochastic epidemic models for emerging diseases

In this thesis several problems concerning the stochastic modelling of emerging infections are considered. Mathematical modelling is often the only available method of predicting the extent of an emerging disease and assessing proposed control measures, as there may be little or no available data on previous outbreaks. Only stochastic models capture the inherent randomness in disease transmission observed in real-life outbreaks, which can strongly influence the outcome of an emerging epidemic because case numbers will initially be small compared with the population size. Chapter 2 considers a model for diseases in which some of the cases exhibit no symptoms and are therefore difficult to observe. Examples of such diseases include influenza, mumps and polio. This chapter investigates the problem of determining whether or not the epidemic has died out if a period containing no symptomatic individuals is observed. When modelling interventions, it is realistic to include a delay between observing the presence of infection and the implementation of control measures. Chapter 3 quantifies the effect that the length of such a delay has on an epidemic amongst a population divided into households. As well as a constant delay, an exponentially distributed delay is also considered. Chapter 4 develops a model for the spread of an emerging strain of influenza in humans. By considering the probability that an outbreak will be contained within a region in which an intervention strategy is active, it becomes possible to quantify and therefore compare the effectiveness of intervention strategies.EThOS - Electronic Theses Online ServiceGBUnited Kingdo