Keywords
SIR model; incidence rate; epidemiology; Lyapunov function, limit cycle
Abstract
A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out limit cycles for important parameter ranges. By ruling out closed orbits, we have an example of two models where mass-action incidence and standard incidence result in distinct qualitative dynamics. Moreover, we develop and generalize a new rational Lyapunov function to prove the global stability of the disease-free equilibrium. Lastly, we define a recovered basic reproduction number, Rε , and show that it captures disease endemicity more accurately than the basic reproduction number, R0, particularly when the birth rate of the population is small.
Thesis Completion Year
2025
Thesis Completion Semester
Spring
Thesis Chair
Shuai, Zhisheng
College
College of Sciences
Department
Mathematics
Thesis Discipline
Mathematics
Language
English
Access Status
Open Access
Length of Campus Access
None
Campus Location
Orlando (Main) Campus
STARS Citation
Shrader, Brendan M., "A Mathematical Modeling Approach to Investigate the Impacts of Post-Infection Mortality and Partial Immunity on Disease Endemicity" (2025). Honors Undergraduate Theses. 241.
https://stars.library.ucf.edu/hut2024/241
Rights Statement
