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UBC Theses and Dissertations

The study of epidemic and endemic diseases using mathematical models David, Jummy Funke


Mathematical models used in epidemiology provides a comprehensive understanding of disease transmission channels and they provide recommendations for methods of control. This thesis uses different mathematical models (direct and indirect transmission models) to understand and analyze different infectious diseases dynamics and possible prevention and/or elimination strategies. As a first step in this research, an age of infection model with heterogeneous mixing and indirect transmission was considered. The simplest form of SIRP epidemic model was introduced and served as a basis for other models. Most mathematical results in this chapter were based on the basic reproduction number and the final size relation. The epidemic model was further extended to incorporate the effect of diffusion using a coupled PDE-ODE system. We proposed a novel approach to modelling air-transmitted diseases using a reduced ODE system, and showed how the reduced ODE system approximates the coupled PDE-ODE system. A deterministic compartmental model of the co-interaction of HIV and infectious syphilis transmission among gay, bisexual and other men who have sex with men (gbMSM) was developed and used to examine the impact of syphilis infection on the HIV epidemic, and vice versa. Analytical expressions for the reproduction number and necessary conditions under which disease-free and endemic equilibria are asymptotically stable were established. Numerical simulations were performed and used to support the analytical results. Finally, the co-interaction model was modified to assess the impact of combining different HIV and syphilis interventions on HIV incidence, HIV prevalence, syphilis incidence and all-cause mortality among gbMSM in British Columbia from 2019 to 2028. Plausible strategies for the elimination of both diseases were evaluated. According to our model predictions and based on the World Health Organization (WHO) threshold for disease elimination as a public health concern, we suggested the most effective strategies to eliminate the HIV and syphilis epidemics over a 10-year intervention period. The results of the research suggest diverse ways in which infectious diseases can be modelled, and possible ways to improve the health of individuals and reduce the overall disease burden, ultimately resulting in improved epidemic control.

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