Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization

Supriadi Putra; Khozin Mu'tamar; Zulkarnain

doi:doi:10.11648/j.ajmcm.20190404.11

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Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization

Supriadi Putra, Khozin Mu'tamar, Zulkarnain

Published in American Journal of Mathematical and Computer Modelling (Volume 4, Issue 4)

Received: 30 September 2019 Accepted: 25 October 2019 Published: 30 October 2019

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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%.

Published in	American Journal of Mathematical and Computer Modelling (Volume 4, Issue 4)
DOI	10.11648/j.ajmcm.20190404.11
Page(s)	83-93
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Growth Mathematical Model, SIR Model, Curve Fitting, PSO Algorithm, Estimation of Parameters

References

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[4]	Sandhya, Kumar, D., Mathematical model for glucose-insulin regulatory system of diabetes mellitus, Advances in Applied Mathematical Biosciences, Vol 2 No 1, 2011.
[5]	Mu'tamar, K., Optimal control strategy for alcoholism model with two infected compartments, IOSR Journal of Mathematics, Vol. 14 Issue 3 Ver. I, 58-67, 2018.
[6]	Shukla, J. B., Singh, G., Shukla, P., Tripathi, A., Modeling and analysis of the effects of antivirus software on an infected computer network, Applied Mathematic and Computation, 227 (2014): 11-18, 2014.
[7]	Kennedy, J. and Eberhart, R. Particle Swarm Optimization. Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948, 1995.
[8]	Bratton, D., Kennedy, J., Defining a standard for particle swarm optimization. Proceeding of the 2007 IEEE Swarm Intelligence Symposium, (1-4244-0708-7/07), 2007.
[9]	Naiborhu, J., Firman, Mu'tamar, K., Particle swarm optimization in the exact linearization technic for output tracking of non-minimum phase nonlinear systems, Applied Mathematical Sciences, Vol. 7 No 109, 5427-5442, 2013.
[10]	Mu'tamar, K., Naiborhu, J., Penentuan matriks pembobot pada kontrol optimal menggunakan adaptive particle swarm optimization, Jurnal Aplikasi Teknologi Universitas Pasir Pengaraian, Vol 8 No 1, 2016.
[11]	Hasni, A. Taibi, R., Draoui, B., Boulard, T., Optimization of greenhouse climate model parameters using particle swarm optimization and genetic algorithms, ScienceDirect: Energy Procidia, 6, 371-380, 2011.
[12]	Jalilvand, A., Kimiyaghalam, A., Ashouri, A., Kord, H., Optimal tunning of PID controller parameters on a DC motor based on advanced particle swarm optimization algorithm, International Journal on technical and physical problems of Engineering, Vol 3 No 4 Issue 9, 10-17, 2011.
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APA Style

Supriadi Putra, Khozin Mu'tamar, Zulkarnain. (2019). Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. American Journal of Mathematical and Computer Modelling, 4(4), 83-93. https://doi.org/10.11648/j.ajmcm.20190404.11

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ACS Style

Supriadi Putra; Khozin Mu'tamar; Zulkarnain. Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. Am. J. Math. Comput. Model. 2019, 4(4), 83-93. doi: 10.11648/j.ajmcm.20190404.11

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AMA Style

Supriadi Putra, Khozin Mu'tamar, Zulkarnain. Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. Am J Math Comput Model. 2019;4(4):83-93. doi: 10.11648/j.ajmcm.20190404.11

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@article{10.11648/j.ajmcm.20190404.11,
  author = {Supriadi Putra and Khozin Mu'tamar and Zulkarnain},
  title = {Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {4},
  pages = {83-93},
  doi = {10.11648/j.ajmcm.20190404.11},
  url = {https://doi.org/10.11648/j.ajmcm.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190404.11},
  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%.},
 year = {2019}
}

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TY  - JOUR
T1  - Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization
AU  - Supriadi Putra
AU  - Khozin Mu'tamar
AU  - Zulkarnain
Y1  - 2019/10/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190404.11
DO  - 10.11648/j.ajmcm.20190404.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 83
EP  - 93
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190404.11
AB  - 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%.
VL  - 4
IS  - 4
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Supriadi Putra, Khozin Mu'tamar, Zulkarnain. (2019). Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. American Journal of Mathematical and Computer Modelling, 4(4), 83-93. https://doi.org/10.11648/j.ajmcm.20190404.11

Copy | Download

ACS Style

Supriadi Putra; Khozin Mu'tamar; Zulkarnain. Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. Am. J. Math. Comput. Model. 2019, 4(4), 83-93. doi: 10.11648/j.ajmcm.20190404.11

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AMA Style

Supriadi Putra, Khozin Mu'tamar, Zulkarnain. Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization. Am J Math Comput Model. 2019;4(4):83-93. doi: 10.11648/j.ajmcm.20190404.11

Copy | Download

@article{10.11648/j.ajmcm.20190404.11,
  author = {Supriadi Putra and Khozin Mu'tamar and Zulkarnain},
  title = {Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {4},
  pages = {83-93},
  doi = {10.11648/j.ajmcm.20190404.11},
  url = {https://doi.org/10.11648/j.ajmcm.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190404.11},
  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%.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization
AU  - Supriadi Putra
AU  - Khozin Mu'tamar
AU  - Zulkarnain
Y1  - 2019/10/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190404.11
DO  - 10.11648/j.ajmcm.20190404.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 83
EP  - 93
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190404.11
AB  - 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%.
VL  - 4
IS  - 4
ER  -

Copy | Download