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UBC Theses and Dissertations
Epidemic modeling of a simple respiratory pathogen Virk, Navjot
Since the emergence of COVID-19, several vaccines have been rolled out at a rapid rate, but the uptake of vaccines is not high enough to eradicate the virus globally. Although most of the population has gotten their vaccines, there is a small number of people who are resistant to receiving vaccine and will never get vaccinated. This is one of the greatest threats to global public health as it could lead to the reemergence of previously eliminated diseases. We proposed a new modified SIR-vaccination model to study the transmission dynamics of COVID-19. We included the impact of individuals who choose to be vaccinated and individuals who choose not to be vaccinated on the final size of the epidemic, in homogeneously and heterogeneously mixed populations. In the homogeneous mixing model, we further analyze two cases: first, where the vaccination campaign has already happened and the second, where the vaccination campaign is happening dynamically during the epidemic. It is shown that both homogeneous and heterogeneous mixing models have a conditionally stable disease-free equilibrium. The reproduction number is derived analytically using the next generation matrix. Using numerical simulations, we investigated the effect of different mixing scenarios between vaccinated and unvaccinated individuals on the final epidemic size and the maximum number of infected people during the epidemic. It is found that as the number of people choosing to never be vaccinated increases, the final epidemic size and the maximum number infected at any time during the epidemic increase as well. We provide interpretation of the results in the context of practical epidemiology, especially vaccination during the epidemic.
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