Volume 4, Issue 4, December 2019, Page: 83-93
Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization
Supriadi Putra, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Khozin Mu'tamar, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Zulkarnain, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Received: Sep. 30, 2019;       Accepted: Oct. 25, 2019;       Published: Oct. 30, 2019
DOI: 10.11648/j.ajmcm.20190404.11      View  45      Downloads  25
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%.
Keywords
Growth Mathematical Model, SIR Model, Curve Fitting, PSO Algorithm, Estimation of Parameters
To cite this article
Supriadi Putra, Khozin Mu'tamar, Zulkarnain, Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization, American Journal of Mathematical and Computer Modelling. Vol. 4, No. 4, 2019, pp. 83-93. doi: 10.11648/j.ajmcm.20190404.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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