# Long term analysis of non-pharmaceutical interventions in SIR model

## Main Article Content

## Abstract

We propose a new epidemiological model, based on the classical SIR model, taking additionally into account a switching prevention strategy. The model has two distinct thresholds that determine the beginning and the end of an intervention and two different transmission rates

## Article Details

How to Cite

Chladná, Z., Kopfová, J., & Rachinskii, D.
(2020).
Long term analysis of non-pharmaceutical interventions in SIR model.

*Proceedings Of The Conference Algoritmy,*, 1 - 10. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1545/809
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Articles

## References

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[2] Z. Chladná , J. Kopfová , D. Rachinskii and S. Rouf, Global dynamics of SIR model with switched transmission rate, J. Math. Biology, (2020), pp. 1209–1233.

[3] B. Dubey, P. Dubey, US. Dubey, Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate. Applications & Applied Mathematics, 10(2), (2015), pp. 718–737.

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[8] N.G. Davies, A.J. Kucharski, R.M. Eggo, A. Gimma, W.J. Edmunds, and CMMID COVID-19 Working Group, The effect of non-pharmaceutical interventions on COVID-19 cases, deaths and demand for hospital services in the UK: a modelling study, (2020), medRxiv.

[9] D. Liberzon, Switching in Systems and Control, Springer-Verlag, New York, (1973).

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Vertical Transmission, Mathematical and Computer Modeling 36 (2002), pp. 1039–1057.

[11] R. Ullah, G. Zaman and S. Islam, Stability analysis of a general SIR epidemic model, VFAST Transactions on Mathematics, Vol. 1, N. 1, (2013), pp. 16–20.

[12] V. Volpert, M. Banerjee, and S. Petrovskii, On a quarantine model of coronavirus infection and data analysis, Mathematical Modelling of Natural Phenomena, 15, (2020), pp. 24.

[13] A. Wang, Y. Xiao, R.A. Cheke, Global dynamics of a piece-wise epidemic model with switching vaccination strategy, Discrete Contin. Dyn. Syst. Ser. B 19, no. 9, (2014), pp.2915–2940.

[14] World Bank Open Data, https://data.worldbank.org/indicator/SP.DYN.CBRT.IN

[2] Z. Chladná , J. Kopfová , D. Rachinskii and S. Rouf, Global dynamics of SIR model with switched transmission rate, J. Math. Biology, (2020), pp. 1209–1233.

[3] B. Dubey, P. Dubey, US. Dubey, Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate. Applications & Applied Mathematics, 10(2), (2015), pp. 718–737.

[4] C. Hou, J. Chen, Y. Zhou, L. Hua, J. Yuan, S. He, Y. Guo, S. Zhang, Q. Jia, C. Zhao, and J. Zhang, The effectiveness f the quarantine of Wuhan city against the Corona Virus Disease 2019 (COVID-19): well mixed SEIR model analysis, Journal of medical virology, (2020), pp. 1–8.

[5] A. Kaddar, Stability analysis in a delayed SIR epidemic model with a saturated incidence rate. Nonlinear Analysis: Modeling and Control, 15(3), (2010), pp. 299–306.

[6] M.J. Keeling, and Pejman Rohani, Modeling infectious diseases in humans and animals Princeton University Press, (2011).

[7] P. Krejčı́, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakuto International Series Mathematical Sciences and Applications, Vol. 8, Gakkōtosho, Tokyo, (1997).

[8] N.G. Davies, A.J. Kucharski, R.M. Eggo, A. Gimma, W.J. Edmunds, and CMMID COVID-19 Working Group, The effect of non-pharmaceutical interventions on COVID-19 cases, deaths and demand for hospital services in the UK: a modelling study, (2020), medRxiv.

[9] D. Liberzon, Switching in Systems and Control, Springer-Verlag, New York, (1973).

[10] Z. Lu and X. Chi, The effect of Constant and Pulse Vaccination on SIR Epidemic Model with Horizontal and

Vertical Transmission, Mathematical and Computer Modeling 36 (2002), pp. 1039–1057.

[11] R. Ullah, G. Zaman and S. Islam, Stability analysis of a general SIR epidemic model, VFAST Transactions on Mathematics, Vol. 1, N. 1, (2013), pp. 16–20.

[12] V. Volpert, M. Banerjee, and S. Petrovskii, On a quarantine model of coronavirus infection and data analysis, Mathematical Modelling of Natural Phenomena, 15, (2020), pp. 24.

[13] A. Wang, Y. Xiao, R.A. Cheke, Global dynamics of a piece-wise epidemic model with switching vaccination strategy, Discrete Contin. Dyn. Syst. Ser. B 19, no. 9, (2014), pp.2915–2940.

[14] World Bank Open Data, https://data.worldbank.org/indicator/SP.DYN.CBRT.IN