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Chaos and Control of COVID-19 Dynamical System

Year 2023, , 233 - 241, 30.11.2023
https://doi.org/10.51537/chaos.1320492

Abstract

Chaos, which is found in many dynamical systems, due to the presence of chaos, systems behave erratically. Due to its erratic behavior, the chaotic behavior of the system needs to be controlled. Severe acute respiratory syndrome Coronavirus 2 (Covid-19), which has spread all over the world as a pandemic. Many dynamical systems have been proposed to understand the spreading behaviour of the disease. This paper investigates the chaos in the outbreak of COVID-19 via an epidemic model. Chaos is observed in the proposed SIR model. The controller is designed based on the fractional-order Routh Hurwitz criteria for fractional-order derivatives. The chaotic behaviour of the model is controlled by feedback control techniques, and the stability of the system is discussed.

References

  • Ahmad, S. W., M. Sarwar, G. Rahmat, K. Shah, H. Ahmad, et al., 2022 Fractional order model for the coronavirus (covid-19) in wuhan, china. Fractals 30: 2240007.
  • Ahmed, E., A. El-Sayed, and H. A. El-Saka, 2006 On some routh– hurwitz conditions for fractional order differential equations and their applications in lorenz, rössler, chua and chen systems. Physics Letters A 358: 1–4.
  • Alsadat, N., M. Imran, M. H. Tahir, F. Jamal, H. Ahmad, et al., 2023 Compounded bell-g class of statistical models with applications to covid-19 and actuarial data. Open Physics 21: 20220242.
  • Babu, G. R., D. Ray, R. Bhaduri, A. Halder, R. Kundu, et al., 2021 Covid-19 pandemic in india: Through the lens of modeling. Global Health: Science and Practice 9: 220–228.
  • Bai, E.-W. and K. E. Lonngren, 2000 Sequential synchronization of two lorenz systems using active control. Chaos, Solitons & Fractals 11: 1041–1044.
  • Borah, M., D. Das, A. Gayan, F. Fenton, and E. Cherry, 2021 Control and anticontrol of chaos in fractional-order models of diabetes, hiv, dengue, migraine, parkinson’s and ebola virus diseases. Chaos, Solitons & Fractals 153: 111419.
  • Borah, M., A. Gayan, J. S. Sharma, Y. Chen, Z. Wei, et al., 2022 Is fractional-order chaos theory the new tool to model chaotic pandemics as covid-19? Nonlinear dynamics 109: 1187–1215.
  • Chandra, S. K. and M. K. Bajpai, 2022 Fractional model with social distancing parameter for early estimation of covid-19 spread. Arabian Journal for Science and Engineering 47: 209–218.
  • Debbouche, N., A. Ouannas, I. M. Batiha, and G. Grassi, 2021 Chaotic dynamics in a novel covid-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. Nonlinear Dynamics pp. 1–13.
  • Farshi, E., 2020 Simulation of herd immunity in covid-19 using monte carlo method. Austin J Pulm Respir Med 7: 1066.
  • Giordano, G., F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, et al., 2020 Modelling the covid-19 epidemic and implementation of population-wide interventions in italy. Nature medicine 26: 855–860.
  • Haq, I. U., N. Ali, H. Ahmad, and T. A. Nofal, 2022 On the fractional-order mathematical model of covid-19 with the effects of multiple non-pharmaceutical interventions. AIMS Math 7: 16017–16036.
  • Higazy, M., 2020 Novel fractional order sidarthe mathematical model of covid-19 pandemic. Chaos, Solitons & Fractals 138: 110007.
  • Javeed, S., S. Anjum, K. S. Alimgeer, M. Atif, M. S. Khan, et al., 2021 A novel mathematical model for covid-19 with remedial strategies. Results in Physics 27: 104248.
  • Kermack, W. O. and A. G. McKendrick, 1927 A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character 115: 700–721.
  • Maltezos, S. and A. Georgakopoulou, 2021 Novel approach for monte carlo simulation of the new covid-19 spread dynamics. Infection, Genetics and Evolution 92: 104896.
  • Mandal, M., S. Jana, S. K. Nandi, A. Khatua, S. Adak, et al., 2020 A model based study on the dynamics of covid-19: Prediction and control. Chaos, Solitons & Fractals 136: 109889.
  • Mangiarotti, S., M. Peyre, Y. Zhang, M. Huc, F. Roger, et al., 2020 Chaos theory applied to the outbreak of covid-19: an ancillary approach to decision making in pandemic context. Epidemiology & Infection 148.
  • Matignon, D., 1996 Stability results for fractional differential equations with applications to control processing. In Computational engineering in systems applications, volume 2, pp. 963–968, Citeseer. Podlubnv, I., 1999 Fractional differential equations academic press. San Diego, Boston 6.
  • Postavaru, O., S. Anton, and A. Toma, 2021 Covid-19 pandemic and chaos theory. Mathematics and Computers in Simulation 181: 138–149.
  • Srivastava, M., S. Agrawal, K. Vishal, and S. Das, 2014 Chaos control of fractional order rabinovich–fabrikant system and synchronization between chaotic and chaos controlled fractional order rabinovich–fabrikant system. Applied Mathematical Modelling 38: 3361–3372.
  • Xie, G., 2020 A novel monte carlo simulation procedure for modelling covid-19 spread over time. Scientific reports 10: 13120.
  • Xu, C., Y. Yu, Y. Chen, and Z. Lu, 2020 Forecast analysis of the epidemics trend of covid-19 in the usa by a generalized fractionalorder seir model. Nonlinear dynamics 101: 1621–1634.
  • Xu, J. and Y. Tang, 2021 An integrated epidemic modelling framework for the real-time forecast of covid-19 outbreaks in current epicentres. Statistical Theory and Related Fields 5: 200–220.
Year 2023, , 233 - 241, 30.11.2023
https://doi.org/10.51537/chaos.1320492

Abstract

References

  • Ahmad, S. W., M. Sarwar, G. Rahmat, K. Shah, H. Ahmad, et al., 2022 Fractional order model for the coronavirus (covid-19) in wuhan, china. Fractals 30: 2240007.
  • Ahmed, E., A. El-Sayed, and H. A. El-Saka, 2006 On some routh– hurwitz conditions for fractional order differential equations and their applications in lorenz, rössler, chua and chen systems. Physics Letters A 358: 1–4.
  • Alsadat, N., M. Imran, M. H. Tahir, F. Jamal, H. Ahmad, et al., 2023 Compounded bell-g class of statistical models with applications to covid-19 and actuarial data. Open Physics 21: 20220242.
  • Babu, G. R., D. Ray, R. Bhaduri, A. Halder, R. Kundu, et al., 2021 Covid-19 pandemic in india: Through the lens of modeling. Global Health: Science and Practice 9: 220–228.
  • Bai, E.-W. and K. E. Lonngren, 2000 Sequential synchronization of two lorenz systems using active control. Chaos, Solitons & Fractals 11: 1041–1044.
  • Borah, M., D. Das, A. Gayan, F. Fenton, and E. Cherry, 2021 Control and anticontrol of chaos in fractional-order models of diabetes, hiv, dengue, migraine, parkinson’s and ebola virus diseases. Chaos, Solitons & Fractals 153: 111419.
  • Borah, M., A. Gayan, J. S. Sharma, Y. Chen, Z. Wei, et al., 2022 Is fractional-order chaos theory the new tool to model chaotic pandemics as covid-19? Nonlinear dynamics 109: 1187–1215.
  • Chandra, S. K. and M. K. Bajpai, 2022 Fractional model with social distancing parameter for early estimation of covid-19 spread. Arabian Journal for Science and Engineering 47: 209–218.
  • Debbouche, N., A. Ouannas, I. M. Batiha, and G. Grassi, 2021 Chaotic dynamics in a novel covid-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. Nonlinear Dynamics pp. 1–13.
  • Farshi, E., 2020 Simulation of herd immunity in covid-19 using monte carlo method. Austin J Pulm Respir Med 7: 1066.
  • Giordano, G., F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, et al., 2020 Modelling the covid-19 epidemic and implementation of population-wide interventions in italy. Nature medicine 26: 855–860.
  • Haq, I. U., N. Ali, H. Ahmad, and T. A. Nofal, 2022 On the fractional-order mathematical model of covid-19 with the effects of multiple non-pharmaceutical interventions. AIMS Math 7: 16017–16036.
  • Higazy, M., 2020 Novel fractional order sidarthe mathematical model of covid-19 pandemic. Chaos, Solitons & Fractals 138: 110007.
  • Javeed, S., S. Anjum, K. S. Alimgeer, M. Atif, M. S. Khan, et al., 2021 A novel mathematical model for covid-19 with remedial strategies. Results in Physics 27: 104248.
  • Kermack, W. O. and A. G. McKendrick, 1927 A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character 115: 700–721.
  • Maltezos, S. and A. Georgakopoulou, 2021 Novel approach for monte carlo simulation of the new covid-19 spread dynamics. Infection, Genetics and Evolution 92: 104896.
  • Mandal, M., S. Jana, S. K. Nandi, A. Khatua, S. Adak, et al., 2020 A model based study on the dynamics of covid-19: Prediction and control. Chaos, Solitons & Fractals 136: 109889.
  • Mangiarotti, S., M. Peyre, Y. Zhang, M. Huc, F. Roger, et al., 2020 Chaos theory applied to the outbreak of covid-19: an ancillary approach to decision making in pandemic context. Epidemiology & Infection 148.
  • Matignon, D., 1996 Stability results for fractional differential equations with applications to control processing. In Computational engineering in systems applications, volume 2, pp. 963–968, Citeseer. Podlubnv, I., 1999 Fractional differential equations academic press. San Diego, Boston 6.
  • Postavaru, O., S. Anton, and A. Toma, 2021 Covid-19 pandemic and chaos theory. Mathematics and Computers in Simulation 181: 138–149.
  • Srivastava, M., S. Agrawal, K. Vishal, and S. Das, 2014 Chaos control of fractional order rabinovich–fabrikant system and synchronization between chaotic and chaos controlled fractional order rabinovich–fabrikant system. Applied Mathematical Modelling 38: 3361–3372.
  • Xie, G., 2020 A novel monte carlo simulation procedure for modelling covid-19 spread over time. Scientific reports 10: 13120.
  • Xu, C., Y. Yu, Y. Chen, and Z. Lu, 2020 Forecast analysis of the epidemics trend of covid-19 in the usa by a generalized fractionalorder seir model. Nonlinear dynamics 101: 1621–1634.
  • Xu, J. and Y. Tang, 2021 An integrated epidemic modelling framework for the real-time forecast of covid-19 outbreaks in current epicentres. Statistical Theory and Related Fields 5: 200–220.
There are 24 citations in total.

Details

Primary Language English
Subjects Structural Biology
Journal Section Research Articles
Authors

Vivek Mishra 0000-0003-1878-9276

Sarit Maitra 0000-0002-0645-4383

Mihir Dash 0000-0002-9790-1117

Saurabh Kumar Agrawal This is me 0000-0003-0623-3596

Praveen Agarwal 0000-0001-7556-8942

Publication Date November 30, 2023
Published in Issue Year 2023

Cite

APA Mishra, V., Maitra, S., Dash, M., Agrawal, S. K., et al. (2023). Chaos and Control of COVID-19 Dynamical System. Chaos Theory and Applications, 5(3), 233-241. https://doi.org/10.51537/chaos.1320492

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

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