IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i5p1177-1184.html
   My bibliography  Save this article

Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period

Author

Listed:
  • Li, Guihua
  • Jin, Zhen

Abstract

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0⩽1, the disease-free equilibrium is globally stable and the disease always dies out. If R0>1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when α1=α2=0 and the disease persists at an endemic equilibrium state if it initially exists.

Suggested Citation

  • Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1177-1184
    DOI: 10.1016/j.chaos.2004.11.062
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905000147
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.11.062?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yongzhen, Pei & Shuping, Li & Shujing, Gao & Min, Zhong, 2017. "Pulse vaccination of an epidemic model with two parallel infectious stages and time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 51-61.
    2. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
    3. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
    4. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    5. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    6. Zhou, Yugui & Xiao, Dongmei & Li, Yilong, 2007. "Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1903-1915.
    7. Zhao, Zhong & Chen, Lansun & Song, Xinyu, 2008. "Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 500-510.
    8. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    9. Mugnaine, Michele & Gabrick, Enrique C. & Protachevicz, Paulo R. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Batista, Antonio M. & Caldas, Iberê L. & Szezech Jr, José D. & V, 2022. "Control attenuation and temporary immunity in a cellular automata SEIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Wang, Yi & Cao, Jinde, 2014. "Global dynamics of multi-group SEI animal disease models with indirect transmission," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 81-89.
    11. Wei, Fengying & Xue, Rui, 2020. "Stability and extinction of SEIR epidemic models with generalized nonlinear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 1-15.
    12. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    13. Zhang, Tailei & Teng, Zhidong, 2009. "Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2411-2425.
    14. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    15. Wen, Luosheng & Yang, Xiaofan, 2008. "Global stability of a delayed SIRS model with temporary immunity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 221-226.
    16. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    17. Weibin Wang & Zeyu Xia, 2023. "Study of COVID-19 Epidemic Control Capability and Emergency Management Strategy Based on Optimized SEIR Model," Mathematics, MDPI, vol. 11(2), pages 1-31, January.
    18. Ndanguza, Denis & Mbalawata, Isambi S. & Haario, Heikki & Tchuenche, Jean M., 2017. "Analysis of bias in an Ebola epidemic model by extended Kalman filter approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 113-129.
    19. Meng, Xinzhu & Jiao, Jianjun & Chen, Lansun, 2009. "Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2114-2125.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    2. Yang, Yali & Li, Jianquan & Ma, Zhien & Liu, Luju, 2010. "Global stability of two models with incomplete treatment for tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 79-85.
    3. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
    4. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    5. Zhang, Tailei & Teng, Zhidong, 2009. "Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2411-2425.
    6. Sun, Chengjun & Lin, Yiping & Tang, Shoupeng, 2007. "Global stability for an special SEIR epidemic model with nonlinear incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 290-297.
    7. Zhou, Yugui & Xiao, Dongmei & Li, Yilong, 2007. "Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1903-1915.
    8. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Wang, Yi & Cao, Jinde, 2014. "Global dynamics of multi-group SEI animal disease models with indirect transmission," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 81-89.
    10. Ilnytskyi, Jaroslav & Pikuta, Piotr & Ilnytskyi, Hryhoriy, 2018. "Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 241-255.
    11. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Liao, Shu & Wang, Jin, 2012. "Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 966-977.
    13. Wen, Luosheng & Yang, Xiaofan, 2008. "Global stability of a delayed SIRS model with temporary immunity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 221-226.
    14. Tewa, Jean Jules & Dimi, Jean Luc & Bowong, Samuel, 2009. "Lyapunov functions for a dengue disease transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 936-941.
    15. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    16. Li, Xue-Zhi & Zhou, Lin-Lin, 2009. "Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 874-884.
    17. Alqarni, M.M. & Mahmoud, Emad E. & Abdel-Aty, Mahmoud & Abualnaja, Khadijah M. & Trikha, Pushali & Jahanzaib, Lone Seth, 2021. "Fractional chaotic cryptovirology in blockchain - analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    18. Yinfeng Chen & Yu Guo & Yaofei Wang & Rongfang Bie, 2022. "Toward Prevention of Parasite Chain Attack in IOTA Blockchain Networks by Using Evolutionary Game Model," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    19. Cai, Liming & Wu, Jingang, 2009. "Analysis of an HIV/AIDS treatment model with a nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 175-182.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1177-1184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.