Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Victoria Gaibor, Senior Kate Moore, Isabel Tejada
Lead Presenter's Name
Victoria Gaibor
Lead Presenter's College
DB College of Arts and Sciences
Faculty Mentor Name
Dr. Hemanta Kunwar
Abstract
This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional simulations are conducted using more realistic values inspired by COVID-19 data. Numerical solutions are visualized to illustrate the evolution of susceptible, infected, and recovered populations over time. Preliminary results show that higher-order methods, such as Runge–Kutta, provide more accurate and stable solutions compared to simpler methods like Euler’s method. The comparison highlights the importance of method selection when modeling real-world phenomena. This project demonstrates how numerical methods can be effectively used to approximate solutions to complex differential equation systems and provides insight into predicting disease spread. The findings have practical significance in understanding epidemic behavior and emphasize the role of computational mathematics in public health modeling.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Epidemiology Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons
Numerical Analysis of the SIR Model for Predicting Disease Spread
This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional simulations are conducted using more realistic values inspired by COVID-19 data. Numerical solutions are visualized to illustrate the evolution of susceptible, infected, and recovered populations over time. Preliminary results show that higher-order methods, such as Runge–Kutta, provide more accurate and stable solutions compared to simpler methods like Euler’s method. The comparison highlights the importance of method selection when modeling real-world phenomena. This project demonstrates how numerical methods can be effectively used to approximate solutions to complex differential equation systems and provides insight into predicting disease spread. The findings have practical significance in understanding epidemic behavior and emphasize the role of computational mathematics in public health modeling.