Heffernan, Jane MarieRuma, Mahmuda Binte Mostofa2026-07-242026-07-242026-04-232026-07-24https://hdl.handle.net/10315/43957Infectious diseases such as HIV, measles, and influenza continue to pose major challenges to global health, particularly in the presence of waning immunity, evolving pathogens, and heterogeneous contact patterns. Understanding the mechanisms driving infection persistence, disease resurgence, and the effectiveness of interventions requires the integration of mathematical modeling. However, an increased level of understanding that modelling can provide here depends on the robustness of the model in (1) it’s representation of the biology and (2) the analyzes and simulation studies that can be conducted to produce quality results. This thesis explores the effects of incorporating biological mechanisms into models of infectious diseases that are often ignored. In the first project we incorporate the virus loss term into a model of pathogen dynamics in-host in order to determine if such a term affects the model dynamics and bifurcation. In the second project we analyze the effects of waning immunity on the probability and severity of measles infections in populations with varying degrees of vaccine-induced immunity. We then extend this waning immunity framework to a study of seasonal influenza. Finally, we explore the effects of environmental reservoirs on the transmissibility of COVID-19, influenza, measles and norovirus in a defined spatial location – a theme park. In all projects we consider deterministic and/or stochastic modelling outcomes, and sensitivity analyses to study the model population dynamics and bifurcations and determine model parameters that most affect population and infection outcomes. By integrating theoretical analysis, numerical simulation, and sensitivity-based methods, this research provides a unified understanding of infection dynamics from within-host to population scales. The findings offer valuable information for designing effective medical and public health intervention strategies.Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.Applied mathematicsEpidemiologyBiologyElectronic Thesis or Dissertation2026-07-24Infectious disease modellingMathematical modelsHIV dynamicsWaning immunityMeasles transmissionInfluenza dynamicsEnvironmental transmissionTheme park transmissionStochastic modelsBifurcation analysisSensitivity analysisStability analysis