IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008220.html
   My bibliography  Save this article

Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments

Author

Listed:
  • Saha, Sangeeta
  • Dutta, Protyusha
  • Samanta, Guruprasad

Abstract

In the present article, global characteristics of a generalized SIRS (susceptible–infected–recovered–susceptible) epidemic model have been investigated incorporating government policy, public response and social behavioral reaction. The effects of environmental fluctuations and time-dependent control strategies on the disease dynamics have also been analyzed. In the case of deterministic model, it is shown that the disease invades in this system when the basic reproduction number (R0) is greater than 1, whereas the dynamics of the stochastic model can be controlled by its associated basic reproduction number R̃s. Specifically, this work emphasizes the importance of nonlinear dynamic analysis of epidemic modeling, as well as the significant impact of social and government actions on disease dynamics. Numerical figure depicts that the governmental action plays a crucial role to control an epidemic situation, and the system turns out to be disease-free sooner if the government takes action at an early stage during a disease outbreak. Furthermore, one of the most key developments is that random fluctuations can prevent disease outbreaks, which can lead to the development of useful control techniques to restrict disease dynamics. The governmental actions and the clinical treatment are considered to be the effective control pair in this model, and it can be observed that the simultaneous implementation of the control strategies significantly reduces the disease burden.

Suggested Citation

  • Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008220
    DOI: 10.1016/j.chaos.2022.112643
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008220
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112643?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. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2022. "A Fractional Order Model to Study the Effectiveness of Government Measures and Public Behaviours in COVID-19 Pandemic," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. Turkyilmazoglu, Mustafa, 2022. "A restricted epidemic SIR model with elementary solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    3. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    4. Saha, Sangeeta & Samanta, G.P., 2019. "Dynamics of an epidemic model with impact of toxins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    5. Saha, Sangeeta & Samanta, G.P., 2019. "Modelling and optimal control of HIV/AIDS prevention through PrEP and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 280-307.
    6. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    7. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A., 2015. "On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 953-976.
    8. Turkyilmazoglu, Mustafa, 2022. "An extended epidemic model with vaccination: Weak-immune SIRVI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    9. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    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. Protyusha Dutta & Nirapada Santra & Guruprasad Samanta & Manuel De la Sen, 2024. "Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread," Mathematics, MDPI, vol. 12(14), pages 1-29, July.

    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. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    2. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    3. Quentin Clairon & Adeline Samson, 2020. "Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 105-127, April.
    4. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    5. Saha, Sangeeta & Samanta, Guruprasad, 2022. "Analysis of a host–vector dynamics of a dengue disease model with optimal vector control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 31-55.
    6. Liu, Songnan & Xu, Xiaojie & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of the DS-I-A model disease with periodic parameter function and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 66-84.
    7. Jang, Gyeong Hwan & Kim, Sung Jin & Lee, Mi Jin & Son, Seung-Woo, 2024. "Effectiveness of vaccination and quarantine policies to curb the spread of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    8. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    9. Huang, Zaitang & Cao, Junfei, 2018. "Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 1-10.
    10. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    11. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    12. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    13. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    14. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    15. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    16. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    17. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    18. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    19. Liu, Meng & Wang, Ke, 2013. "Dynamics and simulations of a logistic model with impulsive perturbations in a random environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 53-75.
    20. 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).

    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:164:y:2022:i:c:s0960077922008220. 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.