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Awareness programs control infectious disease – Multiple delay induced mathematical model

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. 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).
    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. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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).

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