Skip to main content
SpringerLink
Log in

SIQRS Epidemic Modelling and Stability Analysis of COVID-19

  • Chapter
  • First Online:
Predictive and Preventive Measures for Covid-19 Pandemic

Part of the book series: Algorithms for Intelligent Systems ((AIS))

Abstract

In this research article, the spread of COVID-19 due to infectious immigrants with effect of quarantine is investigated using SIQRS epidemic model. The rate of natural death in COVID-19 is embedded in this model. The mathematical equations are solved using Range–Kutta fourth-order method carried by the numerical simulation and graphical interpretation using MATLAB software. We have discussed the stability analysis of infection-free and endemic equilibrium with the help of basic reproduction number. According to the mathematical analysis of Routh–Hurwitz criteria, the system is local asymptotic stable at the equilibrium points when R0 < 1 and unstable when R0 > 1. Moreover, Dulac function and Poincare–Bendixson theorem are applied for the analysis of global stability when R0 > 1. It is also observed from different figures that in a short-term period, the rate of transmission of COVID-19 patients increases. However, in the long run approximately in 120 to 180 days, it becomes stable due to the powerful controlling technique called ‘quarantine or isolation’. The endemic infective class size decreases in Quarantine class, which also leads to disease extinction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

S :

Susceptible class

I :

Infected class

Q :

Quarantine class

R :

Removed class

R o :

Basic reproduction number

α :

Transmission rate per day from S to I

β :

Transmission rate per day from I to Q

γ :

Transmission rate per day from Q to R

σ :

Recovered rate per day from R to S

μ :

Rate of infected immigrant to infected class

θ :

Natural death rate

η :

COVID-19 death rate

References

  1. Al-Sheikh S, Musali F, Alsolamana M (2011) Stability analysis of HIV/AIDS epidemic model with screening. Int Math. Forum 6:3251–3273

    MathSciNet  MATH  Google Scholar 

  2. Horst R (2011) Thieme, global stability of the endemic equilibrium in infinite dimension, lyapunov function and positive operators. J Diff Equ 250:3772–3801

    Article  Google Scholar 

  3. Ma X, Zhou Y, Cao H (2013) Global stability of the endemic equilibrium of discrete SIR epidemic model. Adv Differ Equ. Springer Open Access 42:1–19

    MATH  Google Scholar 

  4. Erdem M, Safan M (2017) Carlos Castillo-Chavez, mathematical analysis of an SIQR influenza model with imperfect quarantine. Bull Math Biol, Springer, pp 1–25

    MATH  Google Scholar 

  5. Lan G, Chen Z, Wei C, Zhang S (2018) Stationary distribution of stochastic SIQR epidemic model with saturated incidence and degenerate diffusion. Phys A 511:61–77

    Article  MathSciNet  Google Scholar 

  6. Cao Z, Zhou S (2018) Dynamical behaviours of stochastic SIQR epidemic model with quarantine adjusted incidence, discrete dynamics in nature and society, pp 1–13

    Google Scholar 

  7. Xia W, Kundu S, Maitra S (2018) Dynamics of delayed SEIQ epidemic model. Adv Differ. Equ. 336:1–21

    MathSciNet  MATH  Google Scholar 

  8. Liu Q, Jiang D, Hayat T, Ahmed B (2018) Stationary distribution and extinction of a stochastic predator-prey model with additional food and nonlinear perturbation. Appl Math Comput 320:226–239

    MathSciNet  MATH  Google Scholar 

  9. Parsamanesh M, Farnoosh R (2018) On global stability of endemic state in an epidemic model with vaccinations. Math Sci 12:313–320

    Article  MathSciNet  Google Scholar 

  10. Bin S, Sun G, Chen C-C (2019) Spread of infectious diseases modelling and analysis of different factors on spread of infectious disease based on cellular automata. Int J Env Res Publ Health 16:1–16

    Article  Google Scholar 

  11. Cakir Z, Savas HB (2020) A mathematical modelling approach in the spread of the novel-2019 corona virus SARS–COV-2(COVID19) pandemic. Electron J Gen Med 17:1–3

    Article  Google Scholar 

  12. Nag S (2020) A mathematical model in the time of COVID-1, March https://doi.org/10.31219/osf.io/8n22hresearchgate.net/publication/330934682

  13. Kuchariski AJ, Russell TW, Diamond C, Liu Y, Edmunds J, Sabstian F, Eggo R (2020) Early dynamics of transmission and control of COVID-19 a mathematical modelling study, March 1–7, 30144–4. https://doi.org/10.1016/s1473-3099(20)

  14. Dey SK, Rahman Md.M, Siddiqi UR, Howldar A (2020) Analyzing the epidemiological outbreak of COVID-19: a visual exploratory data analysis approach. J Med Virology, 1–7. https://doi.org/10.1002/jmv.25743

  15. Shao N, Zhong M, Yan Y, Pan H, Cheng J, Chen W (2020) Dynamic models for COVID-2019 and data analysis. Math Meth Appl Sci wileyonlinelibrary.com/Journal/mma, 1–7

    Google Scholar 

  16. Singh R, Adhikari R (2020) Age structured impact of social distancing on the COVID19 epidemic in India, ARXIV: 2003. 12055VI [9-bio.PE], 1–9

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, S.K.C.G. (Autonomous) College, Paralakhemundi, Odisha, 761200, India

    Aswin Kumar Rauta & Jangyadatta Behera

  2. Department of Mathematics, GIET Ghangapatana, Bhubaneswar, Odisha, 752054, India

    Yerra Shankar Rao

  3. Department of Mathematics, KIST, Jatni, Bhubaneswar, Odisha, 752050, India

    Binayak Dihudi

  4. Department of Mathematics, Ravenshaw University, Cuttack, Odisha, 753003, India

    Tarini Charan Panda

Authors
  1. Aswin Kumar Rauta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yerra Shankar Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jangyadatta Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Binayak Dihudi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tarini Charan Panda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yerra Shankar Rao .

Editor information

Editors and Affiliations

  1. Centre for Developement of Advance Computing (C-DAC), Ministry of Electronics & IT, Mohali, Punjab, India

    Praveen Kumar Khosla

  2. Department of Computer Science and Engineering, G. B. Pant Government Engineering College, New Delhi, India

    Mamta Mittal

  3. Department of Computer Science and Engineering, Amity University, Noida, Uttar Pradesh, India

    Dolly Sharma

  4. Department of Computer Engineering, J. C. Bose University of Science and Technology, Faridabad, India

    Lalit Mohan Goyal

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rauta, A.K., Rao, Y.S., Behera, J., Dihudi, B., Panda, T.C. (2021). SIQRS Epidemic Modelling and Stability Analysis of COVID-19. In: Khosla, P.K., Mittal, M., Sharma, D., Goyal, L.M. (eds) Predictive and Preventive Measures for Covid-19 Pandemic. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-33-4236-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation