Mathematical Models for Emerging Infections in Socially Structured Populations: The Presence of Households and Workplaces

Abstract

This thesis is concerned with the description and analysis of a stochastic model for the spread of a directly transmissible infection, leading to permanent immunity af- ter recovery, in a fully susceptible population with a social structure characterised by the presence of households and workplaces. The model considered is highly ide- alised, but contains the key factors affecting the spread of a directly transmissible infection, namely those environments where frequent and intense contacts are most likely. Important analytical insights include the definition of a novel household re- production number RH, representing the average number of households infected by a single household, which is shown to overcome some of the limitations of a previously defined reproduction number and the development of a methodology for the approximate computation of the real-time growth rate, which is then used for the estimation of RH from the real-time growth rate. An efficient stochastic simulator is described and is used to gain understand- ing of the role that local saturation effects within workplaces play in shaping the epidemic spread and to investigate the reliability of estimates of R0 and the average epidemic final size from the real-time growth rate when the presence of the social structure is neglected. The methodologies are applied to the case of pandemic influenza: its rela- tively low infectiousness suggests that estimation of these key epidemiological quan- tities is surprisingly accurate when the social structure is neglected and that the additional presence of spatial constraints implying geographically localised trans- mission has negligible effect on the overall epidemic dynamics. Despite the lack of reliable data concerning workplaces, a realistic range of possible values for RH is identified, but the efficacy of school closure in reducing transmission appears to be difficult to quantify because of the unknown impact it has on transmission in other workplace environments.