A stochastic model for the spread of infectious diseases within households with intervening preventive treatment.

In Chapter 1 we describe the motivation for the development of a new model for the spread of infectious diseases, we define the statistical problem and briefly review some existing models. In Chapter 2 we develop a general stochastic model for the spread of an infectious disease in households of two when there may be intervening preventive treatment. The distributions of the underlying epidemiological time periods are left arbitrary, while effectiveness of the treatment is considered to be measured both by the resulting modification to individual susceptibility, and by the speed with which it can be administered. Chapter 3 is concerned with possible mathematical representations of the quantities required by the general model. A medically reasonable assumption is demonstrated to produce considerable simplification. In Chapter 4 a simple form of the general model, in which the lengths of both incubation and latent periods are assumed to be constant between individuals, is applied to a detailed set of data for whooping cough. Maximum likelihood estimates of the model's parameters are obtained, the fit of the model is examined and simple medical implications are discussed. Chapter 5 is concerned with fitting some forms of the model, in which the lengths of the incubation and latent periods are allowed to vary, to the whooping cough data. The fits and practicability of these forms are discussed, and compared with those of Chapter 4. In Chapter 6 we suggest further investigations for the whooping cough data, compare our new model with more established ones, and consider how the general form may be simplified in order to apply it to some other infectious diseases. Results from an existing discrete time model which incorporates treatment effects are also examined