Date of Award
Ruaa Al Juboori
The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due to the system's complex eigenvalues.
Sims, Kaylee, "Imperfect Immunity and the Stability of a Modified Kermack-McKendrick Model" (2023). Honors Theses. 2965.