Date of Award

5-25-2019

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics

First Advisor

Jeffrey Ovall

Subjects

Anti-vaccination movement -- Oregon, Anti-vaccination movement -- Washington (State), Virus diseases -- Prevention and control, Vaccination of children -- Mathematical models, Runge-Kutta formulas

DOI

10.15760/honors.712

Abstract

Despite the clear effects and benefits of vaccinations on a population, there are many individuals that choose to not vaccinate for non-medical reasons, giving rise to anti-vaccination movements and vaccine hesitancy. This paper introduces the different types of vaccines and the effects of vaccines in the body and provides an examination of a case study of the 2019 Pacific Northwest measles outbreak. The outbreak is modeled using a proposed modified SIR model and solved using the Fourth-Order Runge-Kutta method. The results suggest that around day 20, almost the entire population becomes infected with the vaccine-resistant strain, which outcompetes the wild-type strain, and the vaccination rate of Clark and Multnomah county suggest that the herd immunity effect does not occur. Many limitations exist for the proposed modified SIR model, with two major limitations being the lack of spatial consideration and the assumption of homogeneous mixing of the population.

Persistent Identifier

https://archives.pdx.edu/ds/psu/28817

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