Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach

W. K. Wong; Filbert H. Juwono

doi:10.23919/JSC.2022.0005

Journal of Social Computing 2022, 3(2): 182-189 https://doi.org/10.23919/JSC.2022.0005

Open Access | Issue | Published: 01 June 2022

Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach

Show Author's Information Hide Author's Information W. K. Wong^¹, Filbert H. Juwono^¹(

)

1 Department of Electrical and Computer Engineering, Curtin University Malaysia, Miri 98009, Malaysia

Keywords:

Susceptible-Infectious-Removed (SIR) model, adaptive differential evolution, Coronavirus Disease 2019 (COVID-19)

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Wong WK, Juwono FH. Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach. Journal of Social Computing, 2022, 3(2): 182-189. https://doi.org/10.23919/JSC.2022.0005

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Abstract

Compartmental pandemic models have become a significant tool in the battle against disease outbreaks. Despite this, pandemic models sometimes require extensive modification to accurately reflect the actual epidemic condition. The Susceptible-Infectious-Removed (SIR) model, in particular, contains two primary parameters: the infectious rate parameter $β$ and the removal rate parameter $γ$ , in addition to additional unknowns such as the initial infectious population. Adding to the complexity, there is an obvious challenge to track the evolution of these parameters, especially $β$ and $γ$ , over time which leads to the estimation of the reproduction number for the particular time window, $R_{T}$ . This reproduction number may provide better understanding on the effectiveness of isolation or control measures. The changing $R_{T}$ values (evolving over time window) will lead to even more possible parameter scenarios. Given the present Coronavirus Disease 2019 (COVID-19) pandemic, a stochastic optimization strategy is proposed to fit the model on the basis of parameter changes over time. Solutions are encoded to reflect the changing parameters of $β_{T}$ and $γ_{T}$ , allowing the changing $R_{T}$ to be estimated. In our approach, an Adaptive Differential Evolution (ADE) and Particle Swarm Optimization (PSO) are used to fit the curves into previously recorded data. ADE eliminates the need to tune the parameters of the Differential Evolution (DE) to balance the exploitation and exploration in the solution space. Results show that the proposed optimized model can generally fit the curves well albeit high variance in the solutions.

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Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach

Show Author's information Hide Author's Information W. K. Wong^¹, Filbert H. Juwono^¹(

)

1 Department of Electrical and Computer Engineering, Curtin University Malaysia, Miri 98009, Malaysia

Abstract

Keywords: Susceptible-Infectious-Removed (SIR) model, adaptive differential evolution, Coronavirus Disease 2019 (COVID-19)

References(23)

T. W. Ng, G. Turinici, and A. Danchin, A double epidemic model for the SARS propagation, BMC Infectious Diseases, vol. 3, no. 19, pp. 1–16, 2003.

DOI Google Scholar

R. U. Din and E. A. Algehyne, Mathematical analysis of COVID-19 by using SIR model with convex incidence rate, Results in Physics, vol. 23, p. 103970, 2021.

DOI Google Scholar

B. Ridenhour, J. M. Kowalik, and D. K. Shay, Unraveling R0: Considerations for public health applications, American Journal of Public Health, vol. 104, no. 2, pp. 32–41, 2014.

DOI Google Scholar

I. Locatelli, B. Trächsel, and V. Rousson, Estimating the basic reproduction number for COVID-19 in western Europe, PLOS ONE, vol. 16, no. 3, pp. 1–9, 2021.

DOI Google Scholar

J. Ren, Y. Yan, H. Zhao, P. Ma, J. Zabalza, Z. Hussain, S. Luo, Q. Dai, S. Zhao, A. Sheikh, et al., A novel intelligent computational approach to model epidemiological trends and assess the impact of non-pharmacological interventions for COVID-19, IEEE Journal of Biomedical and Health Informatics, vol. 24, no. 12, pp. 3551–3563, 2020.

DOI Google Scholar

E. Severeyn, S. Wong, H. Herrera, A. L. Cruz, J. Velásquez, and M. Huerta, Study of basic reproduction number projection of SARS-CoV-2 epidemic in USA and Brazil, in Proc. 2020 IEEE ANDESCON, Quito, Ecuador, 2020, pp. 1–6.https://doi.org/10.1109/ANDESCON50619.2020.9272081

DOI

A. Godio, F. Pace, and A. Vergnano, SEIR modeling of the Italian epidemic of SARS-CoV-2 using computational swarm intelligence, International Journal of Environmental Research and Public Health, vol. 17, no. 10, p. 3535, 2020.

DOI Google Scholar

Z. Huang and Y. Chen, An improved differential evolution algorithm based on adaptive parameter, Journal of Control Science and Engineering, vol. 2013, p. 462706, 2013.

DOI Google Scholar

A. Riccardi, J. Gemignani, F. Fernández-Navarro, and A. Heffernan, Optimisation of non-pharmaceutical measures in COVID-19 growth via neural networks, IEEE Transactions on Emerging Topics in Computational Intelligence, vol. 5, no. 1, pp. 79–91, 2021.

DOI Google Scholar

D. Akman, O. Akman, and E. Schaefer, Parameter estimation in ordinary differential equations modeling via particle swarm optimization, Journal of Applied Mathematics, vol. 2018, p. 9160793, 2018.

DOI Google Scholar

C. Zhan, Z. Wu, Q. Wen, Y. Gao, and H. Zhang, Optimizing broad learning system hyper-parameters through particle swarm optimization for predicting COVID-19 in 184 countries, in Proc. 2020 IEEE International Conference on E-health Networking, Application & Services (HEALTHCOM), Shenzhen, China, 2021, pp. 1–6.

W. Wong and C. I. Ming, A review on metaheuristic algorithms: Recent trends, benchmarking and applications, in Proc. 2019 7^th International Conference on Smart Computing Communications (ICSCC), Sarawak, Malaysia, 2019, pp. 1–5.

I. Cooper, A. Mondal, and C. G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos,Solitons&Fractals, vol. 139, p. 110057, 2020.

DOI

W. K. Wong, F. H. Juwono, and T. H. Chua, SIR simulation of COVID-19 pandemic in Malaysia: Will the vaccination program be effective? https://arxiv.org/abs/2101.07494, 2021.https://doi.org/10.1016/j.chaos.2020.110057

DOI

W. -J. Zhu and S. -F. Shen, An improved SIR model describing the epidemic dynamics of the COVID-19 in China, Results in Physics, vol. 25, p. 104289, 2021.

DOI Google Scholar

E. Barbieri, W. E. Fitzgibbon, and J. Morgan, New insights into an epidemic SIR model for control and public health intervention, in Proc. 2021 IEEE Conference on Control Technology and Applications (CCTA), San Diego, CA, USA, 2021, pp. 150–155.https://doi.org/10.1016/j.rinp.2021.104289

DOI

G. Nakamura, B. Grammaticos, and M. Badoual, Vaccination strategies for a seasonal epidemic: A simple SIR model, Open Communications in Nonlinear Mathematical Physics, doi: 10.46298/ocnmp.7463.https://doi.org/10.1109/CCTA48906.2021.9659144

DOI

H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, vol. 42, no. 4, pp. 599–653, 2000.

DOI Google Scholar

Y. -C. Chen, P. -E. Lu, C. -S. Chang, and T. -H. Liu, A time-dependent SIR model for COVID-19 with undetectable infected persons, IEEE Transactions on Network Science and Engineering, vol. 7, no. 4, pp. 3279–3294, 2020.

DOI Google Scholar

T. V. Inglesby, Public health measures and the reproduction number of SARS-CoV-2, JAMA, vol. 323, no. 21, pp. 2186–2187, 2020.

DOI Google Scholar

S. Das and P. N. Suganthan, Differential evolution: A survey of the state-of-the-art, IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 4–31, 2011.

DOI Google Scholar

N. Noman, D. Bollegala, and H. Iba, An adaptive differential evolution algorithm, in Proc. 2011 IEEE Congress of Evolutionary Computation (CEC), New Orleans, LA, USA, 2011, pp. 2229–2236.https://doi.org/10.1109/CEC.2011.5949891

DOI

S. Das, A. Abraham, and A. Konar, Particle swarm optimization and differential evolution algorithms: Technical analysis, applications and hybridization perspectives, in Advances of Computational Intelligence in Industrial Systems, Y. Liu, A. Sun, H. T. Loh, W. F. Lu, and E. -P. Lim, eds. Berlin, Germany: Springer, 2008, pp. 1–38.https://doi.org/10.1007/978-3-540-78297-1_1

DOI

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Received: 21 April 2022

Revised: 07 June 2022

Accepted: 09 June 2022

Published: 01 June 2022

Issue date: June 2022

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The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).