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UBC Theses and Dissertations

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UBC Theses and Dissertations

Extending Susceptible-Infected-Recovered modeling to COVID-19 Bardwell, Samantha


The onset of the novel coronavirus, SARS-CoV-2, has been trying for both modellers and public health officials as predictions and policies are made amidst the ongoing pandemic. The emergence of new strains, many vaccine-resistant, continue to present modellers with further challenges in predicting the complex infectious disease dynamics. Susceptible-Infected-Recovered (SIR) models are one of the most common models for studying infectious disease. When reinfection is possible, SIRS models are typically used, and have been seen frequently throughout the COVID-19 pandemic. We propose a series of SIRS adaptations to examine waning immunity and reinfection with the evolution of new strains. First, we develop a two-cycle SIRS model with vaccination and varying transmission in which individuals are either immunologically naive and experiencing exposure for the first time, or have some history of exposure, whether through vaccination, infection, or both. The long-run model results are similar to those of the classic SIRS model, predicting an endemic state in which infection exists and all individuals are in the second SIRS cycle. However, implementing two cycles allows for a more detailed transition from pandemic to endemic state. Next, we develop a multi-strain SIRS model, in which new strains are introduced into the population at various time points. Memory exists for the most recent strain exposure, however individuals are susceptible to reinfection for any other strain. We implement a classic SIRS model with varying waning immunity at various time points to represent susceptibility to new strains, and compare this model to our multi-strain model. We find that both models approach the same long-term equilibrium; however, our multi-strain model captures more total infections. Finally, we use a two-strain model to examine the most likely time for a new strain to emerge. Using our two-strain SIRS model, we predict the window of opportunity within which a new strain can be successful with varying transmissibilities, and using an early time stochastic model we investigate the timing of new strain mutation.

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