IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n542154.html

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

Author

Listed:
  • Tongqian Zhang
  • Xinzhu Meng
  • Tonghua Zhang

Abstract

We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection‐free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.

Suggested Citation

  • Tongqian Zhang & Xinzhu Meng & Tonghua Zhang, 2014. "SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:542154
    DOI: 10.1155/2014/542154
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/542154
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/542154?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    3. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
    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. Fulgensia Kamugisha Mbabazi & Joseph Y. T. Mugisha & Mark Kimathi, 2019. "Hopf‐Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).

    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. 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.
    2. 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.
    3. Fulgensia Kamugisha Mbabazi & J. Y. T. Mugisha & Mark Kimathi, 2020. "Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    4. Lei Wang & Zhidong Teng & Long Zhang, 2014. "Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    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. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    7. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    8. 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.
    9. 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.
    10. Haitao Song & Qiaochu Wang & Weihua Jiang, 2014. "Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    11. Chaoqian Wang & Hamdi Kavak, 2022. "A General Epidemic Model and Its Application to Mask Design Considering Different Preferences towards Masks," Complexity, John Wiley & Sons, vol. 2022(1).
    12. Gakkhar, Sunita & Negi, Kuldeep, 2008. "Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 626-638.
    13. Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.
    14. Rao, Xiao-Bo & Zhao, Xu-Ping & Chu, Yan-Dong & Zhang, Jian-Gang & Gao, Jian-She, 2020. "The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. 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.
    16. Kuniya, Toshikazu & Muroya, Yoshiaki, 2015. "Global stability of a multi-group SIS epidemic model with varying total population size," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 785-798.
    17. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    18. 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.
    19. Zhao, Zhen-jun & Liu, Yong-mei & Wang, Ke-xi, 2016. "An analysis of rumor propagation based on propagation force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 263-271.
    20. 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.

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:542154. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.