Comparison of Fourth-Order Runge-Kutta and Second-Order Taylor Series Method for Solving Influenza Cases

Abstract

This study investigates the model of influenza disease transmission using the Fourth Order Runge-Kutta method and Second-Order Taylor Series method. Influenza, a respiratory illness comes from RNA virus that has two forms which is Influenza A and Influenza. Accurate description of Influenza disease requires sophisticated mathematical modelling due to its complexity. The model that utilized in this study is basic SEIR model which includes susceptible, exposed, infected, and recovered population without parameter like the recovery and natural death. Second-Order Taylor Series method utilized in this study because it enhances the basic technique such as Euler Method by using both the first and second derivatives of a function in its calculation. The Fourth-Order Runge-Kutta method also utilized in this study to make a comparison with Second-Order Taylor Series method because the RK4 method utilises four different slopes and uses both first and second derivatives at the beginning of each step to calculate its next value. The model was executed using MATLAB software, which produces numerical solutions that simulate the dynamics of influenza disease transmission. Second Order Taylor Series method gives significantly better  precision compared to Euler’s method; however, it is slightly less accurate than the Fourth-Order Runge-Kutta (RK4) method while RK4 method gives greater accuracy and stability because it involves four functions evaluations per time step, but it also demands more computational effort. While the number of susceptible continuously declines, the exposed population peaks as infected population increasing and recovery populations grows. The accuracy of both methods shows its potential for handling 
complex disease transmission models. In conclusion, this research validates and compare the accuracy of both methods in modelling influenza disease cases providing insights for public health interventions. To comprehend and manage disease dynamics, the results highlight the significance of precise numerical techniques, paving the way for more robust epidemiological modelling.