Investigation of SIS epidemics on dynamic network models with temporary link deactivation control schemes

Jun Hyung Bae; Sang-Mook Lee; Jun Hyung Bae; Sang-Mook Lee

doi:10.3934/mbe.2022295

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 6: 6317-6330. doi: 10.3934/mbe.2022295

Previous Article Next Article

Research article Special Issues

Investigation of SIS epidemics on dynamic network models with temporary link deactivation control schemes

Jun Hyung Bae ¹,
Sang-Mook Lee ^{2
,
,}

1.
Interdisciplinary Program in Computational Science and Technology, Seoul National University, Seoul 08826, Korea
2.
Department of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea

Academic Editor: Masaki Ogura

Received: 02 March 2022 Revised: 06 April 2022 Accepted: 12 April 2022 Published: 19 April 2022

Mathematical modeling of epidemic diseases is increasingly being used to respond to emerging diseases. Although conditions modeled by SIS dynamics will eventually reach either a disease-free steady-state or an endemic steady state without interventions, it is desirable to eradicate the disease as quickly as possible by introducing a control scheme. Here, we investigate the control methods of epidemic models on dynamic networks with temporary link deactivation. A quick link deactivation mechanism can simulate a community effort to reduce the risk of infection by temporarily avoiding infected neighbors. Once infected individuals recover, the links between the susceptible and recovered are activated. Our study suggests that a control scheme that has been shown ineffective in controlling dynamic network models may yield effective responses for networks with certain types of link dynamics, such as the temporary link deactivation mechanisms. We observe that a faster and more effective eradication could be achieved by updating control schemes frequently.
- SIS epidemics,
- dynamic networks,
- individual-based modeling
Citation: Jun Hyung Bae, Sang-Mook Lee. Investigation of SIS epidemics on dynamic network models with temporary link deactivation control schemes[J]. Mathematical Biosciences and Engineering, 2022, 19(6): 6317-6330. doi: 10.3934/mbe.2022295

Related Papers:

Abstract

Mathematical modeling of epidemic diseases is increasingly being used to respond to emerging diseases. Although conditions modeled by SIS dynamics will eventually reach either a disease-free steady-state or an endemic steady state without interventions, it is desirable to eradicate the disease as quickly as possible by introducing a control scheme. Here, we investigate the control methods of epidemic models on dynamic networks with temporary link deactivation. A quick link deactivation mechanism can simulate a community effort to reduce the risk of infection by temporarily avoiding infected neighbors. Once infected individuals recover, the links between the susceptible and recovered are activated. Our study suggests that a control scheme that has been shown ineffective in controlling dynamic network models may yield effective responses for networks with certain types of link dynamics, such as the temporary link deactivation mechanisms. We observe that a faster and more effective eradication could be achieved by updating control schemes frequently.

References

[1]	Centers for Disease Control and Prevention, Nonpharmaceutical Interventions (NPIs), 2021. Available from: https://www.cdc.gov/nonpharmaceutical-interventions/index.html.
[2]	Á. Bodó, P. L Simon, Control of epidemic propagation on networks by using a mean-field model : Dedicated to Professor László Hatvani on the occasion of his 75th birthday, Electron. J. Qual. Theory Differ. Equation, (2018), 1–13. https://doi.org/10.14232/ejqtde.2018.1.41 doi: 10.14232/ejqtde.2018.1.41
[3]	D. J. Daley, J. Gani, Epidemic modelling: an introduction, Cambridge University Press, 2001.
[4]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Math. Phys., 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
[5]	I. Z. Kiss, J. C. Miller, P. L. Simon, Mathematics of Epidemics on Networks, Springer, 2017.
[6]	W. Yang, D. Zhang, L. Peng, C. Zhuge, L. Hong, Rational evaluation of various epidemic models based on the COVID-19 data of China, medRxiv, (2020), https://doi.org/10.1101/2020.03.12.20034595 doi: 10.1101/2020.03.12.20034595
[7]	F. Brauer, C. Castillo-Chávez, Basic ideas of mathematical epidemiology, in Mathematical Models in Population Biology and Epidemiology, (2001), 275–337.
[8]	A. L. Barabási, R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509–512. https://doi.org/10.1126/science.286.5439.509 doi: 10.1126/science.286.5439.509
[9]	D. J. Watts, S. H. Strogatz, Collective dynamics of 'small-world' networks, Nature, 393 (1998), 440–442. https://doi.org/10.1038/30918 doi: 10.1038/30918
[10]	M. J. Keeling, K. T. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), 295–307. https://doi.org/10.1098/rsif.2005.0051 doi: 10.1098/rsif.2005.0051
[11]	I. Tunc, M. S. Shkarayev, L. B. Shaw, Epidemics in adaptive social networks with temporary link deactivation, J. Stat. Phys., 151 (2013), 355–366. https://doi.org/10.1007/s10955-012-0667-7 doi: 10.1007/s10955-012-0667-7
[12]	R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1992.
[13]	M. J. Keeling, D. A. Rand, A. J. Morris, Correlation models for childhood epidemics, Proc. Royal Soc. B, 264 (1997), 1149–1156. https://doi.org/10.1098/rspb.1997.0159 doi: 10.1098/rspb.1997.0159
[14]	M. J. Keeling, The effects of local spatial structure on epidemiological invasions, Proc. Royal Soc. B, 266 (1999), 859–867. https://doi.org/10.1098/rspb.1999.0716 doi: 10.1098/rspb.1999.0716
[15]	P. Erdős, A. Rényi, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 17–60.
[16]	T. Gross, C. J. D. D'Lima, B. Blasius, Epidemic dynamics on an adaptive network, Phys. Rev. Lett., 96 (2006), 208701. https://doi.org/10.1103/PhysRevLett.96.208701 doi: 10.1103/PhysRevLett.96.208701
[17]	R. Pastor-Satorras, A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200–3203. https://doi.org/10.1103/PhysRevLett.86.3200 doi: 10.1103/PhysRevLett.86.3200
[18]	V. Grimm, S. F. Railsback, Individual-Based Modeling and Ecology, Princeton University Press, 2005.
[19]	S. F. Railsback, V. Grimm, Agent-Based and Individual-Based Modeling: A Practical Introduction, Princeton University Press, 2019.
[20]	F. Sélley, Á. Besenyei, I. Z. Kiss, P. L. Simon, Dynamic control of modern, network-based epidemic models, SIAM J. Appl. Dyn. Syst., 14 (2015), 168–187. https://doi.org/10.1137/130947039 doi: 10.1137/130947039
[21]	L. Grüne, J. Pannek, Nonlinear Model Predictive Control. Communications and Control Engineering, Springer, 2011.
[22]	A. Gray, D. Greenhalgh, L. Hu, X. Mao, J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math., 71 (2011), 876–902. https://doi.org/10.1137/10081856X doi: 10.1137/10081856X

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)