Chaos and Control of COVID-19 Dynamical System
Year 2023,
, 233 - 241, 30.11.2023
Vivek Mishra
,
Sarit Maitra
,
Mihir Dash
,
Saurabh Kumar Agrawal
Praveen Agarwal
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
Vivek Mishra
,
Sarit Maitra
,
Mihir Dash
,
Saurabh Kumar Agrawal
Praveen Agarwal
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.