Globular clusters are not simple stellar populations. Practically all globular clusters show multiple populations (MPs), where at the same metallicity [Fe/H], approximately half of their stars are enriched by the products of high-temperature hydrogen burning relative to the rest that show field-like abundances. The source of enrichment for forming the enriched population is an unresolved problem. Interacting massive binaries are an underexplored proposed source of enrichment. Many assessments of the theory are based on only one modelled binary. We simulate a suite of metal-intermediate, [Fe/H]=-1.44, interacting binaries with initial primary masses of 10 to 40 solar masses, with mass ratios ranging from 0.15 to 0.9, over periods ranging from about 2 to 700 days using MESA. Our simulations show that binaries at higher masses, higher mass ratios, and near our upper period limit tend to be the most enriching with ejecta showing HeNaCNOAlMg variations consistent with hot-H burning. Some binaries do not eject material, suggesting binary mass loss can contribute to the dilution of enrichment. As a realistic population, binaries within our parameter space eject about ten times as much mass as they would as single stars. Ejection occurs on timescales of about 11 Myr, consistent with observed and theoretical limits on the age spreads for MPs. Our systems are rare, making them more suited to explaining the stochastic nature of MPs but not the large fraction of enriched stars. Spreads in He, N, Na, C, and Al for our ejecta could reasonably explain the observed spreads in clusters. Reduced variation in O and Mg suggests more massive binaries should be investigated. A multi-scale approach to cluster formation with multiple types of enrichment sources is a necessary next step for validating MP formation scenarios. / Thesis / Master of Science (MSc) / The majority of stars form in star clusters. Globular clusters are the oldest and most massive type of star cluster. Formerly thought to be made of stars of the same age and chemical composition, nearly all observed globular clusters are now known to host multiple populations. About half of their stars form from similar material as isolated stars. The other half show signs of enrichment. How enriched stars get their enriching material is an open problem in cluster formation. Pairs of stars orbiting each other as binaries were proposed to eject the material needed to form these stars. We model 408 binaries to find that some systems eject large amounts of enrichment, especially when the stars are more massive. The rarity of these systems suggests binaries can explain the variations seen in multiple populations between clusters but cannot fully explain the large fraction of enriched stars seen.

Mass gatherings stress local and global health care systems as they bring together individuals from all over the world that have very different health conditions. We firstly provide an overview of the concepts and results of mathematical epidemiology and public health. Secondly, we present an introduction to the mathematical modelling of measles using deterministic and stochastic approaches for both single and multiple populations. Lastly, we develop a model for mass gatherings and present an application to measles during the Hajj by studying an SIR deterministic metapopulation model with residency and its stochastic analogue. The models incorporate real world country data and time dependent movement and transmission rates, accounting for realistic volume of international travel and seasonality of measles activity. Numerical results for the deterministic system are presented. We conclude with a discussion on further work.

Mass gatherings stress local and global health care systems as they bring together individuals from all over the world that have very different health conditions. We firstly provide an overview of the concepts and results of mathematical epidemiology and public health. Secondly, we present an introduction to the mathematical modelling of measles using deterministic and stochastic approaches for both single and multiple populations. Lastly, we develop a model for mass gatherings and present an application to measles during the Hajj by studying an SIR deterministic metapopulation model with residency and its stochastic analogue. The models incorporate real world country data and time dependent movement and transmission rates, accounting for realistic volume of international travel and seasonality of measles activity. Numerical results for the deterministic system are presented. We conclude with a discussion on further work.