IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v251y2015icp539-563.html
   My bibliography  Save this article

Awareness programs control infectious disease – Multiple delay induced mathematical model

Author

Listed:
  • Greenhalgh, David
  • Rana, Sourav
  • Samanta, Sudip
  • Sardar, Tridip
  • Bhattacharya, Sabyasachi
  • Chattopadhyay, Joydev

Abstract

We propose and analyze a mathematical model to study the impact of awareness programs on an infectious disease outbreak. These programs induce behavioral changes in the population, which divide the susceptible class into two subclasses, aware susceptible and unaware susceptible. The system can have a disease-free equilibrium and an endemic equilibrium. The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived. We further improve and study the model by introducing two time-delay factors, one for the time lag in memory fading of aware people and one for the delay between cases of disease occurring and mounting awareness programs. The delayed system has positive bounded solutions. We study various cases for the time delays and show that in general the system develops limit cycle oscillation through a Hopf bifurcation for increasing time delays. We show that under certain conditions on the parameters, the system is permanent. To verify our analytical findings, the numerical simulations on the model, using realistic parameters for Pneumococcus are performed.

Suggested Citation

  • Greenhalgh, David & Rana, Sourav & Samanta, Sudip & Sardar, Tridip & Bhattacharya, Sabyasachi & Chattopadhyay, Joydev, 2015. "Awareness programs control infectious disease – Multiple delay induced mathematical model," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 539-563.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:539-563
    DOI: 10.1016/j.amc.2014.11.091
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314016233
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.11.091?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Wang, Yi & Cao, Jinde & Jin, Zhen & Zhang, Haifeng & Sun, Gui-Quan, 2013. "Impact of media coverage on epidemic spreading in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5824-5835.
    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. Basir, Fahad Al & Ray, Santanu & Venturino, Ezio, 2018. "Role of media coverage and delay in controlling infectious diseases: A mathematical model," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 372-385.
    2. Shin, Hyelim & Lee, Taesik, 2025. "Effectiveness of social distancing under partial compliance of individuals," European Journal of Operational Research, Elsevier, vol. 322(3), pages 949-959.
    3. 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.
    4. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    5. Weike Zhou & Yanni Xiao & Jane Marie Heffernan, 2019. "Optimal media reporting intensity on mitigating spread of an emerging infectious disease," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-18, March.
    6. Zhang, Zizhen & Rahman, Ghaus ur & Gómez-Aguilar, J.F. & Torres-Jiménez, J., 2022. "Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    8. Yao Hongxing & Zou Yushi, 2019. "Research on Rumor Spreading Model with Time Delay and Control Effect," Journal of Systems Science and Information, De Gruyter, vol. 7(4), pages 373-389, August.
    9. Kar, Silajit & Maiti, Dilip K. & Maiti, Atasi Patra, 2024. "Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence," Chaos, Solitons & Fractals, Elsevier, vol. 178(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, 2023. "When reality bites: Local deaths and vaccine take-up," European Economic Review, Elsevier, vol. 156(C).
    2. 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.
    3. Carol Horton Tremblay & Davina C. Ling, 2005. "AIDS education, condom demand, and the sexual activity of American youth," Health Economics, John Wiley & Sons, Ltd., vol. 14(8), pages 851-867, August.
    4. 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.
    5. Han, Dun & Sun, Mei, 2014. "Can memory and conformism resolve the vaccination dilemma?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 95-104.
    6. Battiston, Pietro & Gamba, Simona, 2021. "COVID-19: R0 is lower where outbreak is larger," Health Policy, Elsevier, vol. 125(2), pages 141-147.
    7. Toxvaerd, Flavio, 2010. "Recurrent Infection and Externalities in Prevention," CEPR Discussion Papers 8112, C.E.P.R. Discussion Papers.
    8. 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.
    9. 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).
    10. Daniel S. Hamermesh, 1999. "The Art of Labormetrics," NBER Working Papers 6927, National Bureau of Economic Research, Inc.
    11. 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.
    12. 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.
    13. 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.
    14. Kai Barron & Charles D. H. Parry & Debbie Bradshaw & Rob Dorrington & Pam Groenewald & Ria Laubscher & Richard Matzopoulos, 2024. "Alcohol, Violence, and Injury-Induced Mortality: Evidence from a Modern-Day Prohibition," The Review of Economics and Statistics, MIT Press, vol. 106(4), pages 938-955, July.
    15. 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).
    16. 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).
    17. Francis, Andrew M. & Mialon, Hugo M., 2010. "Tolerance and HIV," Journal of Health Economics, Elsevier, vol. 29(2), pages 250-267, March.
    18. 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.
    19. Alison L. Sexton Ward & Timothy K. M. Beatty, 2016. "Who Responds to Air Quality Alerts?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(2), pages 487-511, October.
    20. Noel Rapa, 2021. "Mitigation measures, prevalence response and public mobility during the COVID-19 emergency," CBM Working Papers WP/03/2021, Central Bank of Malta.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:eee:apmaco:v:251:y:2015:i:c:p:539-563. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.