Mathematical models for respiratory syncytial virus (RSV) transmission

Respiratory syncytial virus (RSV) causes respiratory tract infections in infants and young children. Almost all children experience an RSV infection within the first two years of life, and while mortality due to RSV infection is low in developed countries, the virus presents a significant burden in Australia and internationally. In temperate regions, RSV displays strong seasonal patterns. In Perth, Western Australia, RSV detections show a distinct biennial cycle, and similar patterns have been observed in other temperate locations. While there is no licensed vaccine for RSV, there are several candidates in clinical trials. Understanding the seasonal patterns of RSV, and developing mathematical models that capture key transmission characteristics, can assist with planning the future rollout of an RSV vaccine. This thesis focusses on three themes: age structure and immunity; seasonality and climate; and vaccination. For the first theme, I present age-structured compartmental mathematical models with waning immunity and seasonal forcing. I fit these models to RSV data for Perth and explore the parameter space and bifurcation structures. The models help explain the different patterns in RSV detections observed globally. In particular, both the seasonality and immunity parameters must exceed certain thresholds for the model to produce biennial patterns, which aligns with observed data. Further, I identify a ‘window’ of birth rate parameters that produces biennial patterns, showing that RSV seasonality may not be only driven by weather and climatic factors as was previously thought. The second research theme involves a time series analysis of both RSV and bronchiolitis data, as approximately 70\% of bronchiolitis hospitalisations are linked to RSV infection. First, I identify a clear shift in seasonality for both RSV and bronchiolitis, from the temperate to tropical regions of Western Australia. I then apply a mathematical time series analysis method, complex demodulation, to assess the validity of using bronchiolitis hospitalisations as a proxy for RSV cases. I find bronchiolitis and RSV are similar in terms of timing, but that epidemic magnitudes differ. To address the third research theme, I adapt the compartmental model to incorporate a finer age structure, contact patterns and naturally-derived maternal immunity, to assess the potential impact of a maternal vaccination strategy for RSV in Perth. I find that the introduction of a maternal vaccine is unlikely to alter the regular biennial RSV pattern, but that the vaccine would be effective in reducing hospitalisations due to RSV in children younger than six months of age. This thesis adopts both mathematical modelling and data analysis approaches to improve our understanding of RSV dynamics. Developing mathematical models for RSV transmission in the Australian context allows a better understanding of the relative importance of age cohorts, immunity, climatic factors, and demography, in driving different RSV epidemic patterns. Further, data analysis shows the extent to which bronchiolitis hospitalisations are representative of RSV detections, and that different approaches to interventions must be considered in temperate versus tropical Western Australia. These findings will be instrumental in planning an effective vaccine rollout strategy for Western Australia