Abstract
Susceptible, Infected and Resistant (SIR) models are used to observe the spread of infection from infected populations into healthy populations. Stability analysis of the model is done using the Routh-Hurwitz criteria, basic reproduction number or the Lyapunov Stability. For stability analysis, parameters value are needed and these values are usually assumed. Given data cannot be used to determine the parameter values of SIR model because analytic solution of system of nonlinear differential equation cannot be determined. In this article, we determine the parameters of the exponential growth model, logistic model and SIR models using the Particle Swarm Optimization (PSO) algorithm. The SIR model is solved numerically using the Euler method based on the parameter values determined by PSO. The simulation results show that the PSO algorithm is good enough in determining the parameters of the three models compared to analytical methods and the Gauss-Newton’s method. Based on the average hypothesis test the relative error obtained from the PSO algorithm to determine the parameters is less than 3% with a significance level of 1%.
Highlights
Mathematical models can be interpreted as mathematical equations that explain behavior in the real world
The logistic model has again determined its numerical solution for the comparative test of the success of the Particle Swarm Optimization (PSO) method in determining parameters, (4) determining the parameter values of each model where the PSO method is used for the whole model, the linear curve fitting method for exponential and logistic models, while the Gauss-Newton’s method only for exponential models, (5) comparing data and function results based on the generated parameter values, (6) for the SIR epidemic model, the data obtained by simulation with predetermined parameter values
This article has discussed the determination of parameters in the exponential, logistical and SIR epidemic models using the PSO algorithm
Summary
Mathematical models can be interpreted as mathematical equations that explain behavior in the real world. In addition to the human environment, the SIR model can be used to analyze the spread of viruses in a computer environment [6] If this mathematical model is combined with data, mathematics can be an excellent tool for environmental observation and the basis for policy making. To process data and mathematical models in the form of ordinary differential equations is not easy. This is because the process uses the curve fitting which has so far only been carried out on functions that have an explicit form. It is difficult to do in the SIR model because this model cannot be solved analytically so the solution of the equation in the explicit form cannot be determined
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