Numerical Simulation of Infectious Disease Spread Using the SIR Model: an Application of Euler's Method

The spread of infectious diseases is a very complex phenomenon and requires mathematical modeling to understand the dynamics of the spread. One of the common approaches used to model the spread of diseases is the SIR (Susceptible-Infected-Recovered) model. This study aims to implement numerical methods, especially the Euler method, to simulate the spread of infectious diseases using the SIR model. This study focuses on the application of Euler's Method to solve differential equations that describe the changes in infected, susceptible, and recovered populations in a finite system. The Euler method is used to calculate the numerical solution of the system with a small time step. The simulation results show how the spread of the disease can be predicted in various scenarios, with sensitivity analysis to model parameters such as transmission rate and recovery rate. These simulations provide insight into the dynamics of the disease and help in designing more effective public health policies. In conclusion, the Euler’s method has proven to be a useful tool for modeling and predicting the spread of diseases, although the accuracy of the results is highly dependent on the choice of time step. Further research can examine the application of other numerical methods and their comparison with analytical models to improve prediction and accuracy in real applications.