IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i5p1151-1157.html
   My bibliography  Save this article

Modal series solution for an epidemic model

Author

Listed:
  • Acedo, L.
  • González-Parra, Gilberto
  • Arenas, Abraham J.

Abstract

In this article, we generalize a recently proposed method to obtain an exact general solution for the classical Susceptible, Infected, Recovered and Susceptible (SIRS) epidemic mathematical model. This generalization is based upon the nonlinear coupling of two frequencies in an infinite modal series solution. It is shown that these series provide a nonstandard approach in order to obtain an accurate analytical solution for the classical SIRS epidemic model. Numerical results of the SIRS epidemic model for real and complex frequencies are included in order to test the validity and reliability of the method. This method could be applied to a wide class of models in physics, chemistry or engineering.

Suggested Citation

  • Acedo, L. & González-Parra, Gilberto & Arenas, Abraham J., 2010. "Modal series solution for an epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1151-1157.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:5:p:1151-1157
    DOI: 10.1016/j.physa.2009.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109009133
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2009.11.003?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. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    2. Jódar, Lucas & Villanueva, Rafael J. & Arenas, Abraham J. & González, Gilberto C., 2008. "Nonstandard numerical methods for a mathematical model for influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 622-633.
    Full references (including those not matched with items on IDEAS)

    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. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    2. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    3. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    5. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    6. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    7. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
    8. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "SDE SIS epidemic model with demographic stochasticity and varying population size," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 218-238.
    9. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 684-704.
    10. Serrano, Daniel Hernández & Villarroel, Javier & Hernández-Serrano, Juan & Tocino, Ángel, 2023. "Stochastic simplicial contagion model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Witbooi, Peter J., 2013. "Stability of an SEIR epidemic model with independent stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4928-4936.
    13. Zhao, Laijun & Wang, Qin & Cheng, Jingjing & Zhang, Ding & Ma, Ting & Chen, Yucheng & Wang, Jiajia, 2012. "The impact of authorities’ media and rumor dissemination on the evolution of emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3978-3987.
    14. Adamu, Elias M. & Patidar, Kailash C. & Ramanantoanina, Andriamihaja, 2021. "An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 171-190.
    15. Liu, Qun & Chen, Qingmei, 2016. "Dynamics of a stochastic SIR epidemic model with saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 155-166.
    16. Xin Jiang, 2021. "Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    17. Yang, Jin & Tan, Yuanshun & Cheke, Robert A., 2019. "Modelling effects of a chemotherapeutic dose response on a stochastic tumour-immune model," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 1-13.
    18. Khalsaraei, Mohammad Mehdizadeh & Shokri, Ali & Ramos, Higinio & Heydari, Shahin, 2021. "A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 397-410.
    19. El Fatini, Mohamed & El Khalifi, Mohamed & Gerlach, Richard & Laaribi, Aziz & Taki, Regragui, 2019. "Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. María Ángeles Castro & Miguel Antonio García & José Antonio Martín & Francisco Rodríguez, 2019. "Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems," Mathematics, MDPI, vol. 7(11), pages 1-14, November.

    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:phsmap:v:389:y:2010:i:5:p:1151-1157. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.