Archive
Special Issues 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
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
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
Reference

Osemwinyen, A. C., Diakhaby, A., Mathematical modelling of the transmission dynamics of Ebola virus, Applied and Computational Mathematics, 4 (4): 313-320, 2015.

Bonyah, E., Okosun, K. O., Mathematical modeling of Zika virus, Asian Pasific Journal of Tropical Disease, 6 (9): 673-679, 2016.

Gebremeskel, A. A., Krogstad, H. E., Mathematical modeling of Endemic Malaria Transmission, American Journal of Applied Mathematics, 3 (2): 36-46, 2015.

Sandhya, Kumar, D., Mathematical model for glucose-insulin regulatory system of diabetes mellitus, Advances in Applied Mathematical Biosciences, Vol 2 No 1, 2011.

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.

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.

Kennedy, J. and Eberhart, R. Particle Swarm Optimization. Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948, 1995.

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.

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.

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.

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.

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.

Chiu, C. C., Cheng, Y. T., Chang, C. W., Comparison of particle swarm optimization and genetic algorithm for the path loss reduction in an urban area, Journal of applied science and engineering, Vol 15 No 4, pp. 371-380, 2012.

Solihin, M. I., Akmeliawati, R., Particle swarm optimization for stabilizing controller of self-erecting linear inverted pendulum, International Journal of Electrical and Electronic Systems Research, Vol. 3, 13-23, 2010.

Quantitative Environmental Learning Project at Seattle Central College [Online Data Sets]. Available: https://seattlecentral.edu/qelp/sets/026/026.html.

Quantitative Environmental Learning Project at Seattle Central College [Online Data Sets]. Available: https://seattlecentral.edu/qelp/sets/015/015.html. 