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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
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
Al-Sheikh S, Musali F, Alsolamana M (2011) Stability analysis of HIV/AIDS epidemic model with screening. Int Math. Forum 6:3251–3273
Horst R (2011) Thieme, global stability of the endemic equilibrium in infinite dimension, lyapunov function and positive operators. J Diff Equ 250:3772–3801
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
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
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
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
Xia W, Kundu S, Maitra S (2018) Dynamics of delayed SEIQ epidemic model. Adv Differ. Equ. 336:1–21
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
Parsamanesh M, Farnoosh R (2018) On global stability of endemic state in an epidemic model with vaccinations. Math Sci 12:313–320
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
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
Nag S (2020) A mathematical model in the time of COVID-1, March https://doi.org/10.31219/osf.io/8n22hresearchgate.net/publication/330934682
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)
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
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
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
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
DOI: https://doi.org/10.1007/978-981-33-4236-1_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-33-4235-4
Online ISBN: 978-981-33-4236-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)