Stability analysis of the SEIRS epidemic model with infectious dynamics during latent and infectious periods

Guichen Lu, Yifan Miao

Article ID: 2885
Vol 2, Issue 2, 2024
DOI: https://doi.org/10.54517/mss2885
Received: 15 August 2024; Accepted: 13 September 2024; Available online: 30 September 2024;
Issue release: 15 November 2024

VIEWS - 3827 (Abstract)

Download PDF

Abstract

Coronary pneumonia caused by the SARS-CoV-2 virus was one of the most significant public health threats in recent years. In this paper, we develop and investigate an SEIRS epidemic model that incorporates infectivity during both the latent and infectious stages to characterize the transmission dynamics of COVID-19. By calculating the basic reproduction number (R0) and applying monotonic dynamical system theory along with geometric methods, we validate the threshold theorem. Our analysis demonstrates that the disease-free equilibrium is globally stable when R0 < 1, while the endemic equilibrium becomes globally stable when R0 > 1.

Keywords

COVID-19; SEIRS epidemic model; Basic reproduction number; Global stability


References

1. Alrashed S, Min-Allah N, Saxena A, et al. Impact of Lockdowns on the Spread of COVID-19 in Saudi Arabia. Informatics in Medicine Unlocked. 2020; 20: 100420.

2. Annas S, Pratama MI, Rifandi M, et al. Stability analysis and numerical aimulation of SEIR Model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons and Fractals. 2020; 139: 110072.

3. Jiao J, Liu Z, Cai S. Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible. Applied Mathematics Letters. 2020; 107: 106442.

4. Kyrychko YN, Blyuss KB, Brovchenko I. Mathematical modelling of the dynamics and containment of COVID-19 in Ukraine. Sci Rep. 2020; 10: 19662.

5. Zu J, Li ML, Li ZF, et al. Transmission patterns of COVID-19 in the mainland of China and the efficacy of different control strategies: A data- and model-driven study. Infect Dis Poverty. 2020; 9: 83.

6. Zamir M, Shah K, Nadeem F, et al. Threshold Conditions for Global Stability of Disease Free State of COVID-19. Results in Physics. 2021; 21: 103784.

7. Abdullah, Ahmad S, Owyed S, et al. Mathematical analysis of COVID-19 via new mathematical model. Chaos, Solitons Fractals, Chaos, Solitons and Fractals. 2021; 143: 110585.

8. Al-arydah M. Assessing vaccine efficacy for infectious diseases with variable immunity using a mathematical model. Sci Rep. 2024; 14: 18572.

9. Bouissa A, Tahiri M, Tsouli N, et al. Global dynamics of a time-fractional spatio-temporal SIR model with a generalized incidence rate. J. Appl. Math. Comput. 2023; 69: 4779–4804.

10. Bouissa A and Tsouli N. Comprehensive analysis of disease dynamics using nonlinear fractional order SEIRS model with Crowley-Martin functional response and saturated treatment. International Journal of Biomathematics. 2024; 2350114.

11. Liu W, Hethcote HW, Levin SA. Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 1987; 25: 359–380.

12. Al-arydah M, Berhe H, Dib K, Madhu K. Mathematical modeling of the spread of the coronavirus under strict social restrictions. Math Meth Appl Sci. 2021; 1–11.

13. Van den Driessche P and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences. 2002; 180: 29–48.

14. Jiang J. On the Global Stability of Cooperative Systems. Bulletin of the London Mathematical Society. 1994; 5: 455–458.

15. Thieme HR. Convergence results and a Poincar-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 1992; 30: 755–C763.

16. Cheng Y and Yang X. On the global stability of SEIRS models in epidemiology. Can. Appl. Math. Q. 2012; 20: 115–133.

17. Li M, Muldowney JS. Global stability for the SEIR model in epidemiology. Math. Biosci. 1995; 125: 155–164.

18. Li M, Muldowney JS. A Geometric Approach to Global-Stability Problems. SIAM J. Math. Anal. 1996; 27: 1070– 1083.

19. Li M, Muldowney JS, van den Driessche P. Global stability of SEIRS models in epidemiology. Can. Appl. Math. Q. 1999; 7: 409–425.

20. Lu G and Lu Z. Geometric approach to global asymptotic stability for the SEIRS models in epidemiology. Nonl. Anal. RWA. 2017; 36: 20–43.

21. Li G, Jin Z. Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. Chaos, Solitons and Fractals. 2005; 25: 1177–1184.

22. Li G, Wang W, Jin Z. Global stability of an SEIR epidemic model with constant immigration. Chaos, Solitons and Fractals. 2006; 30: 1012–1019.

23. Li M, Graef JR, Wang L, Karsai, J. Global dynamics of a SEIR model with varying total population size. Mathematical biosciences. 1999; 160: 191–213.

24. Li M, Muldowney JS. Dynamics of differential equations on invariant manifolds. J. Differential Equations. 2000; 168: 295–320.

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Guichen Lu, Yifan Miao

License URL: https://creativecommons.org/ licenses/by/4.0/
Guidelines
For authors For reviewers For editors
Useful Links
Crossref Similarity Check Creative Commons
About
About the publisher Other journals Contact
©Copyright 2019 - 2024 by Asia Pacific Academy of Science Pte. Ltd. All Rights Reserved Privacy Policy Open Access Disclaimer