Mathematical models are a fundamental component of many epidemiological studies. While models of infectious disease are well established, there are evident methodological gaps when attempting to provide realistic descriptions of particular biological systems. In this thesis we probe questions related to two global public health problems, zoonotic influenza and depression, requiring innovative modelling approaches to be developed, analysed and fitted to data. We give particular consideration to parameter inference schemes to gain insights into the dynamics of these illnesses, and model simulation for validation and prediction purposes, including assessing intervention impact. First, we investigate zoonotic influenza transmission at a local scale, our example being H5N1 in Bangladesh. It is vital to devise new models incorporating zoonotic transmission, and establish the factors enabling both continued transmission within poultry and spillover across the poultry-human divide. We outline a set of candidate transmission models, with a zoonotic transmission component, parameterised with a Bayesian inference scheme using data from two H5N1 outbreaks in the Dhaka region. Applied at two distinct spatial scales, we elucidate the model considerations that best capture the size and spatial distribution of reported cases. Simulations then illustrate the predicted impact of interventions designed to reduce H5N1 transmission. Second, the emergence of influenza strains with pandemic potential is considered from a global viewpoint. Using a Bayesian model selection approach we compare plausible model hypotheses regarding the mechanisms driving influenza pandemic occurrences. Analysing the time periods between putative influenza pandemics since 1700, it is shown the weight of evidence favours influenza pandemic emergence being history-dependent, rather than a memoryless process. Predictive distributions are then presented for the expected number of pandemic events from 2010 to 2110. Third, spread of behaviour-linked health problems are amenable to being represented with methodological approaches typically used to model infectious diseases. We explore this with regards to depression, using a longitudinal dataset comprising information on both the in-school friendships and mood status of US adolescents. A novel model is described that exploits the dynamical behaviour of mood over time to ascertain which mood states spread on social networks, via a contagion-like mechanism, and which do not.
Suggested citation: Edward M. Hill. (2017) Mathematical modelling approaches for spreading processes: zoonotic influenza and social contagion. PhD thesis, University of Warwick, UK.