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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen
Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen
Student Research Submissions
Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. …
Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt
Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt
Student Research Submissions
In this research project, we used numerical methods to investigate trends in the susceptible, exposed, infectious, quarantined, recovered, closed cases and insusceptible populations for the COVID-19 pandemic in 2021. We used the SEIQR model containing seven ordinary differential equations, based on the SIR model for epidemics. An analytical solution was derived from a simplified version of the model, created by making various assumptions about the original model. Numerical solutions were generated for the first 100 days of 2021 using algorithms based on Euler's Method, Runge-Kutta Method, and Multistep Methods. Our goal is to show that numerical methods can help us …