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Role of media coverage and delay in controlling infectious diseases: A mathematical model

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  • Basir, Fahad Al
  • Ray, Santanu
  • Venturino, Ezio

Abstract

The aim of this paper is to investigate the effect of awareness coverage and delay in controlling infectious diseases. We formulate an SIS model considering individuals’ behavioral changes due to the influences of media coverage and divide the susceptible class into two subclasses: aware susceptible and unaware susceptible. Other model variables are infected human and media campaign. It is assumed that the rate of becoming aware (unaware), from unaware to aware susceptible human (from aware to unaware susceptible human), is a function of media campaign. A time delay is considered for the time that is taken by an unaware (aware) susceptible individual to become aware (unaware). An additional time delay is considered due to the time lag needed in organising awareness campaigns. The model exhibits two equilibria: the disease-free equilibrium and the endemic equilibrium. The disease-free equilibrium is stable if the basic reproduction number is smaller than unity and the endemic equilibrium exhibits a Hopf-bifurcation, in both delayed and non-delayed system, whenever it exists. Analytical and numerical results prove the significance of awareness and delay on the prevalence of infectious diseases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:372-385
    DOI: 10.1016/j.amc.2018.05.042
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    References listed on IDEAS

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    1. Markus Frölich & Rosalia Vazquez-Alvarez, 2009. "HIV/AIDS Knowledge and Behaviour: Have Information Campaigns Reduced HIV Infection? The Case of Kenya," African Development Review, African Development Bank, vol. 21(1), pages 86-146.
    2. Unknown, 2014. "Media Coverage 2014," 2014: Ethics, Efficiency and Food Security: Feeding the 9 Billion, Well, 26-28 August 2014 225573, Crawford Fund.
    3. 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.
    4. Lixia Zuo & Maoxing Liu, 2014. "Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
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    Cited by:

    1. Abraha, Teklebirhan & Al Basir, Fahad & Obsu, Legesse Lemecha & Torres, Delfim F.M., 2021. "Pest control using farming awareness: Impact of time delays and optimal use of biopesticides," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ray, Santanu & Basir, Fahad Al, 2020. "Impact of incubation delay in plant–vector interaction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 16-31.
    3. Fahad Al Basir & Teklebirhan Abraha, 2023. "Mathematical Modelling and Optimal Control of Malaria Using Awareness-Based Interventions," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    4. 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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