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Global stability of an SEI epidemic model with general contact rate

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  • Li, Guihua
  • Zhen, Jin

Abstract

This paper consider an SEI epidemic model with general contact rate that incorporates constant recruitment and have infectious force in the latent period and infected period. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium and the epidemic equilibrium by using the Poincarè–Bendixson property.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:3:p:997-1004
    DOI: 10.1016/j.chaos.2004.06.012
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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).
    13. 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).
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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).
    19. 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).
    20. 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.

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