Robust Mathematical Modelling of Household-Stratified Epidemic Time-series

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Infectious diseases affect us all, and are one of the main risks to human health and quality of life worldwide. Despite advances in our understanding of them, a great many questions remain about the way in which infectious diseases actually transmit through human populations. Some open questions, even for common diseases like influenza, relate to estimation of quite basic quantities: how infectious is the illness in different contexts; how long cases of different ages are infectious for; and how much immunity to re-infection is conferred upon recovery.Other more fundamental questions relate to more subtle issues. Many human pathogen species are differentiated into strains that can be identified using modern laboratory techniques, but the way that these interact with each other - for example, whether previous infection with one strain confers immunity to another - is complex and hard to determine. At the same time, the relationship between severity of illness, and how infectious as case is, can be quite complex.Answering these and other questions requires study of disease transmission in a natural setting, but simply measuring the amount of illness in a population does not yield sufficient information to resolve them. Conducting a household cohort study, which involves measuring infections in several whole households over time, offers the promise of much more information. Such studies are being run with increasing frequency.This project is about developing the mathematics needed to analyse household cohort studies in a way that extracts as much novel epidemiological information as possible. There are several steps to be taken: a first question might be how likely a given set of study results are to be observed if we knew every relevant quantity. By creating methods to calculate such a quantity efficiently on a computer, it can become possible to invert the process and gain insight into the epidemiological mechanisms that generate the data.Ultimately, by knowing more about the way in which diseases spread through the human population, we can improve our control of them. For example, if new cases of a disease do not become infectious for several days, then this gives time for quarantine to be an effective control measure. If within-household transmission is much more intense than between-household transmission, then interventions should be focused on the household.