Date Thesis Awarded

5-2023

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Leah Shaw

Committee Members

Junping Shi

Jeffrey Shields

Abstract

For many organisms, births occur in seasonal pulses, which can affect how infection persists within a population. Population changes throughout the year can also change the per capita predation rates, which in turn can affect disease dynamics. The use of pulsed birth rates in addition to more accurate predation functions increases the realism of models, which is crucial for preventing or controlling major disease outbreaks. This research uses a Susceptible-Infected (SI) model to study the effects of seasonal births and predation on the spread of infection in a population over time. We consider models with constant and pulsed births as well as linear and hyperbolic predation functions. We calculate the basic reproductive number to determine the conditions under which infection fades out or spreads and use numerical simulations to examine system behavior when infection is able to persist. We find that when predation depends linearly on prey populations, the timing of births does not affect average infection or disease transmissibility. However, this is not the case for systems with hyperbolic predation. Additionally, we observe that hyperbolic predation is more conducive to successful infection invasion in a population compared to linear predation.

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