Journal Home >

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, $RT$. This reproduction number may provide better understanding on the effectiveness of isolation or control measures. The changing $RT$ 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 $βT$ and $γT$, allowing the changing $RT$ 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.

Abstract
Full text
Outline

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

Show Author's information Filbert H. Juwono1( )
Department of Electrical and Computer Engineering, Curtin University Malaysia, Miri 98009, Malaysia

## 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, $RT$. This reproduction number may provide better understanding on the effectiveness of isolation or control measures. The changing $RT$ 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 $βT$ and $γT$, allowing the changing $RT$ 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.

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

## References(23)

1

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.

2

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.

3

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.

4

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.

5

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.

6
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
7

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.

8

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.

9

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.

10

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.

11
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 &amp; Services (HEALTHCOM), Shenzhen, China, 2021, pp. 1–6.
12
W. Wong and C. I. Ming, A review on metaheuristic algorithms: Recent trends, benchmarking and applications, in Proc. 2019 7th International Conference on Smart Computing Communications (ICSCC), Sarawak, Malaysia, 2019, pp. 1–5.
13

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.

14
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
15

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.

16
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
17
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
18

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

19

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.

20

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

21

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.

22
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
23
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
Publication history
Rights and permissions