Mathematical Modeling of Vaccinations: Modified SIR Model, Vaccination Effects, and Herd Immunity [open pdf - 250KB]
From the 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 [susceptible, infected, and recovered] 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."
University Honors Theses, Paper 695
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