Mathematical Biology Seminar
2-3 p.m., Wednesday, April 10, 2024
MSB 318
Speaker:
Brendan Shrader
Department of Mathematics
University of Central Florida
Title: Investigating the impact of Long-COVID and other post-infection conditions on long-term infectious disease dynamics.
Abstract: The recent COVID-19 pandemic highlights the importance of understanding how post-infection mortality affects disease dynamics. This is because a significant proportion of COVID-19 survivors continue to experience persistent symptoms, known as “Long-COVID,” enduring for years after initial infection. In this talk, we discuss a mass-action infectious disease model that models Long-COVID by incorporating post-infection mortality and partial immunity. We then construct a new model that assumes the disease is transmitted by the standard incidence rate. For this new model, we prove the existence and uniqueness of the endemic equilibrium, prove the global stability of the disease-free equilibrium, and provide partial results about the global stability of the endemic equilibrium. Then, we compare the two models, with particular attention to the existence of limit cycles. It is found that in cases where limit cycles occur in the mass-action model, they do not occur in our standard incidence model. Lastly, we discuss the relationship between partial immunity and the endemicity of infectious diseases using simulations. Our findings highlight how incidence rates qualitatively change the dynamics of disease models and how partial immunity impacts disease severity.
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