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Date of Award

Spring 2023

Rights

Access perpetually restricted to EWU users with an active EWU NetID

Document Type

Thesis: EWU Only

Department

Mathematics

Abstract

Infectious diseases have been a persistent challenge to global health throughout history, and they continue to pose a significant threat in the present day. With the emergence of new diseases and the reemergence of existing ones, understanding the transmission dynamics, and developing effective prevention strategies are critical for public health. Mathematical modeling has proven to be a valuable tool in studying infectious diseases, allowing researchers to simulate and analyze various scenarios to gain insights into disease spread and inform public health policies. This paper provides an overview of the different types of mathematical models utilized in infectious disease modeling, focusing on their application in studying the spread of complex diseases such as Plague, Polio, and Covid-19. Mathematical models can capture the intricacies of disease transmission by incorporating factors such as population demographics, disease characteristics, and intervention strategies. By quantifying these variables, researchers can simulate the dynamics of disease transmission and assess the impact of various interventions, such as vaccination campaigns, social distancing measures, or treatment protocols. To ensure the reliability of these models, statistical techniques are employed to validate their accuracy and assess their goodness of fit to real-world data. Model fitting involves comparing the simulated outputs with observed epidemiological data, allowing researchers to refine their models and improve their predictive capabilities. Moreover, understanding the stability of steady states in these models is crucial in predicting the long-term behavior of an outbreak. By analyzing the stability of these states, researchers can determine whether an outbreak will be self-limiting or persist within the population over time. By studying diseases like Plague, Polio, and Covid-19, this research aims to provide valuable insights into the spread of infectious diseases and contribute to the development of effective intervention strategies. The findings from this study can enhance our understanding of disease transmission dynamics and help inform public health efforts to prevent and control future epidemics. Ultimately, the goal is to minimize the impact of infectious diseases on populations worldwide and ensure the well-being of individuals and communities.

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