Imperfect Immunity and the Stability of a Modified Kermack-McKendrick Model

Author

Kaylee SimsFollow

Date of Award

Spring 5-12-2023

Document Type

Undergraduate Thesis

Department

Mathematics

First Advisor

Samuel Lisi

Second Advisor

Laura Sheppardson

Third Advisor

Ruaa Al Juboori

Relational Format

Dissertation/Thesis

Abstract

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.

Recommended Citation

Sims, Kaylee, "Imperfect Immunity and the Stability of a Modified Kermack-McKendrick Model" (2023). Honors Theses. 2965.
https://egrove.olemiss.edu/hon_thesis/2965

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