IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v157y2019icp77-99.html
   My bibliography  Save this article

Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment

Author

Listed:
  • Kumar, Anuj
  • Srivastava, Prashant K.
  • Gupta, R.P.

Abstract

The present study of a nonlinear compartmental SVIR model accounts for the dynamics of infectious diseases in population. In this model, the effect of information on vaccination coverage is quantified when medical resources are limited during the epidemic outbreak. Model analysis is performed and the global asymptotic stability of the disease free equilibrium is established when treatment is available for all infective individuals. However, the existence of multiple endemic equilibria is observed due to saturation in medical treatment and information-induced vaccination coverage. If the basic reproduction number is greater than unity, a unique endemic equilibrium for the model is obtained under some parametric conditions. Using the geometric approach, the global asymptotic stability of this endemic equilibrium is established under a parametric constraint. Further, when medical resources are limited, the existence Hopf bifurcation is shown analytically, which infers the oscillatory persistence of disease within the population. Occurrence of Hopf–Hopf bifurcation is also investigated numerically. At first Hopf bifurcation threshold, an endemic equilibrium loses its stability and produces oscillations, and further, it regains its stability at another Hopf bifurcation threshold when oscillations disappear. Hence, multiple stability switches are observed due to the saturated treatment and information-induced vaccination. The effect of the fading of memory also plays a crucial role and gives rise to complex dynamical behaviour and also affects the stability properties. Numerically, different types of backward bifurcation are also examined. Extensive numerical experimentations are also carried out to further explore the model system.

Suggested Citation

  • Kumar, Anuj & Srivastava, Prashant K. & Gupta, R.P., 2019. "Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 77-99.
    • Handle: RePEc:eee:matcom:v:157:y:2019:i:c:p:77-99
    DOI: 10.1016/j.matcom.2018.09.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418302696
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.09.024?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. 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.
    2. Tomas Philipson, 1996. "Private Vaccination and Public Health: An Empirical Examination for U.S. Measles," Journal of Human Resources, University of Wisconsin Press, vol. 31(3), pages 611-630.
    3. Avner Ahituv & V. Joseph Hotz & Tomas Philipson, 1996. "The Responsiveness of the Demand for Condoms to the Local Prevalence of AIDS," Journal of Human Resources, University of Wisconsin Press, vol. 31(4), pages 869-897.
    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. 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.
    2. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Pan Tang & Shiwen Qian & Lei Shi & Longxing Qi & Tingting Li, 2023. "The Influence of Migration to Regions with Different Coverages of Health Education on Schistosomiasis," Mathematics, MDPI, vol. 11(12), pages 1-27, June.
    4. Kumar, Anuj & Srivastava, Prashant K. & Dong, Yueping & Takeuchi, Yasuhiro, 2020. "Optimal control of infectious disease: Information-induced vaccination and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).

    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. Giulietti, Corrado & Vlassopoulos, Michael & Zenou, Yves, 2021. "When Reality Bites: Local Deaths and Vaccine Take-Up," GLO Discussion Paper Series 999, Global Labor Organization (GLO).
    2. Battiston, Pietro & Gamba, Simona, 2021. "COVID-19: R0 is lower where outbreak is larger," Health Policy, Elsevier, vol. 125(2), pages 141-147.
    3. Celidoni, Martina & Costa-Font, Joan & Salmasi, Luca, 2023. "Mobility restrictions and alcohol use during lockdown: “A still and dry pandemic for the many”?," Economics & Human Biology, Elsevier, vol. 50(C).
    4. John Mullahy, 1999. "It'll only hurt a second? Microeconomic determinants of who gets flu shots," Health Economics, John Wiley & Sons, Ltd., vol. 8(1), pages 9-24, February.
    5. Graff Zivin, Joshua & Neidell, Matthew, 2009. "Days of haze: Environmental information disclosure and intertemporal avoidance behavior," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 119-128, September.
    6. Giulietti, Corrado & Vlassopoulos, Michael & Zenou, Yves, 2023. "When reality bites: Local deaths and vaccine take-up," European Economic Review, Elsevier, vol. 156(C).
    7. Matthew Neidell, 2009. "Information, Avoidance Behavior, and Health: The Effect of Ozone on Asthma Hospitalizations," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    8. Momota, Akira & Tabata, Ken & Futagami, Koichi, 2005. "Infectious disease and preventive behavior in an overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1673-1700, October.
    9. Auld, M. Christopher, 2003. "Choices, beliefs, and infectious disease dynamics," Journal of Health Economics, Elsevier, vol. 22(3), pages 361-377, May.
    10. Sarkar, Jayanta, 2022. "Do disease prevalence and severity drive COVID-19 vaccine demand?," Economic Analysis and Policy, Elsevier, vol. 75(C), pages 310-319.
    11. Celidoni, Martina & Costa-Font, Joan & Salmasi, Luca, 2023. "Mobility Restrictions and Alcohol Use during Lockdown: 'A Still and Dry Pandemic for the Many'?," IZA Discussion Papers 16251, Institute of Labor Economics (IZA).
    12. Celidoni, Martina & Costa-Font, Joan & Salmasi, Luca, 2023. "Mobility restrictions and alcohol use during lockdown: "a still and dry pandemic for the many"?," LSE Research Online Documents on Economics 119467, London School of Economics and Political Science, LSE Library.
    13. Kai Barron & Luis F. Gamboa & Paul Rodríguez-Lesmes, 2019. "Behavioural Response to a Sudden Health Risk: Dengue and Educational Outcomes in Colombia," Journal of Development Studies, Taylor & Francis Journals, vol. 55(4), pages 620-644, April.
    14. Hussey, Andrew & Nikolsko-Rzhevskyy, Alex & Walker, Jay, 2010. "AIDing Contraception: HIV and Recent Trends in Abortion Rates," MPRA Paper 20895, University Library of Munich, Germany.
    15. Toxvaerd, Flavio, 2010. "Recurrent Infection and Externalities in Prevention," CEPR Discussion Papers 8112, C.E.P.R. Discussion Papers.
    16. Pronkina, Elizaveta & Berniell, Inés & Fawaz, Yarine & Laferrère, Anne & Mira, Pedro, 2023. "The COVID-19 curtain: Can past communist regimes explain the vaccination divide in Europe?," Social Science & Medicine, Elsevier, vol. 321(C).
    17. Daniel S. Hamermesh, 1999. "The Art of Labormetrics," NBER Working Papers 6927, National Bureau of Economic Research, Inc.
    18. Pierluigi Diotaiuti & Giuseppe Valente & Stefania Mancone & Lavinia Falese & Fernando Bellizzi & Daniela Anastasi & Elisa Langiano & Fábio Hech Dominski & Alexandro Andrade, 2021. "Perception of Risk, Self-Efficacy and Social Trust during the Diffusion of Covid-19 in Italy," IJERPH, MDPI, vol. 18(7), pages 1-17, March.
    19. Sok Chul Hong & Eunju Lee & Seojung Oh, 2023. "Unintended health benefits of adopting preventive behaviors during a virus outbreak," Health Economics, John Wiley & Sons, Ltd., vol. 32(2), pages 324-342, February.
    20. Matthew Goodkin-Gold & Michael Kremer & Christopher M. Snyder & Heidi L. Williams, 2020. "Optimal Vaccine Subsidies for Endemic and Epidemic Diseases," Working Papers 2020-162, Becker Friedman Institute for Research In Economics.

    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:matcom:v:157:y:2019:i:c:p:77-99. 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/mathematics-and-computers-in-simulation/ .

    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.