Comparative Analysis of Influenza Model Solutions Using Euler, Heun, and RK4 Methods
Keywords: Euler, Heun, influenza model, numerical method, Runge-Kutta
Abstract
This study explores the numerical solutions of an influenza epidemiological model, specifically the SEIR (Susceptible, Exposed, Infected, and Recovered) type, which is represented by a system of nonlinear differential equations. Three numerical methods were applied to solve this model: the Euler method, Heun’s method, and the fourth-order Runge-Kutta (RK4) method. The solutions obtained from these numerical methods were compared to the reference solution from ODE45, as the exact solution of the SEIR model remains unknown. Numerical simulations revealed that using either a very large step size ( ) or a very small step size led to significant numerical errors. Among the five different step sizes tested, provided the most accurate results. Based on the average computational time across different step sizes, the Euler method was the fastest, while RK4 was the slowest. However, the Euler method exhibited the largest error margin, whereas Heun’s and RK4 methods produced comparable errors. Although Heun’s method had the same error margin as RK4, it required less computational time, making it the most efficient choice for this case.
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References
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