IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v219y2024icp50-86.html
   My bibliography  Save this article

The impact of social media advertisements and treatments on the dynamics of infectious diseases with optimal control strategies

Author

Listed:
  • Kumar, Arjun
  • Dubey, Uma S.
  • Dubey, Balram

Abstract

The dissemination of public health information through television and social media posts is essential for informing the public about the transmission of contagious diseases, which is crucial in preventing the spread of various infectious diseases. In this paper, we propose a non-linear mathematical model to assess the effect of advertisements through social media in creating awareness and limiting treatment on spreading infectious diseases. These initiatives may alter population behaviour and divide the susceptible population into subgroups. In addition, to comprehend these dynamics better, we use half-saturation constant rates for media coverage and treatment. The model’s well-posedness and feasibility are evaluated. The possible biological equilibrium points are calculated. Local and global stability are carried out. The objective of our study is to produce the model’s bifurcation. Transcritical, Saddle–node, Hopf bifurcation of codimension 1 and Cusp, Generalized-Hopf (Bautin), and Bogdanov–Takens (BT) bifurcation of codimension 2 are studied for this purpose. Due to the limited medical resources and supply efficiency, the model exhibits backward bifurcation, resulting in bistability. Moreover, the occurrence condition for stability and direction of Hopf bifurcation is discussed. This model study demonstrates that the system is significantly influenced by the pace with which awareness programmes are implemented and that raising this value above a threshold may result in continuous oscillation. Sensitivity analysis employs the normalized forward sensitivity index of the basic reproduction number to provide a comprehensive understanding of the effect of various parameters on accelerating and limiting disease spread. Further, the minimum possible cost is determined by formulating an optimal control system based on sensitivity analysis and applying Pontryagin’s maximum principle. Methods of cost-effectiveness, such as ACER and ICER, are used to determine the most cost-effective control intervention strategy among all the strategies. Numerical simulations have been done to support all theoretical findings.

Suggested Citation

  • Kumar, Arjun & Dubey, Uma S. & Dubey, Balram, 2024. "The impact of social media advertisements and treatments on the dynamics of infectious diseases with optimal control strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 50-86.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:50-86
    DOI: 10.1016/j.matcom.2023.12.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423005220
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.12.015?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. 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).
    2. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. Lacitignola, Deborah & Saccomandi, Giuseppe, 2021. "Managing awareness can avoid hysteresis in disease spread: an application to coronavirus Covid-19," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Ghosh, Jayanta Kumar & Biswas, Sudhanshu Kumar & Sarkar, Susmita & Ghosh, Uttam, 2022. "Mathematical modelling of COVID-19: A case study of Italy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 1-18.
    6. Oluwaseun Sharomi & Tufail Malik, 2017. "Optimal control in epidemiology," Annals of Operations Research, Springer, vol. 251(1), pages 55-71, April.
    7. Zaman, Gul & Kang, Yong Han & Cho, Giphil & Jung, Il Hyo, 2017. "Optimal strategy of vaccination & treatment in an SIR epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 63-77.
    Full references (including those not matched with items on IDEAS)

    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. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Khatun, Mst Sebi & Das, Samhita & Das, Pritha, 2023. "Dynamics and control of an SITR COVID-19 model with awareness and hospital bed dependency," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Lacitignola, Deborah & Diele, Fasma, 2021. "Using awareness to Z-control a SEIR model with overexposure: Insights on Covid-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Tingqiang Chen & Lei Wang & Jining Wang & Qi Yang, 2017. "A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency," Complexity, Hindawi, vol. 2017, pages 1-16, December.
    5. Chen, Yi & Wang, Lianwen & Zhang, Jinhui, 2024. "Global asymptotic stability of an age-structured tuberculosis model: An analytical method to determine kernel coefficients in Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    7. Svetlana Kolesnikova & Ekaterina Kustova, 2023. "Application of a Stochastic Extension of the Analytical Design of Aggregated Regulators to a Multidimensional Biomedical Object," Mathematics, MDPI, vol. 11(21), pages 1-20, October.
    8. Abidemi, Afeez & Ackora-Prah, Joseph & Fatoyinbo, Hammed Olawale & Asamoah, Joshua Kiddy K., 2022. "Lyapunov stability analysis and optimization measures for a dengue disease transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    9. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    10. Li, Tingting & Guo, Youming, 2022. "Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    11. Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Xu, Yuan-Hao & Wang, Hao-Jie & Lu, Zhong-Wen & Hu, Mao-Bin, 2023. "Impact of awareness dissemination on epidemic reaction–diffusion in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    13. Juang, Jonq & Liang, Yu-Hao, 2024. "Epidemic models in well-mixed multiplex networks with distributed time delay," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    14. Chen, Ya & Zhang, Juping & Jin, Zhen, 2023. "Optimal control of an influenza model with mixed cross-infection by age group," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 410-436.
    15. Juliano Marçal Lopes & Coralys Colon Morales & Michelle Alvarado & Vidal Augusto Z. C. Melo & Leonardo Batista Paiva & Eduardo Mario Dias & Panos M. Pardalos, 2022. "Optimization methods for large-scale vaccine supply chains: a rapid review," Annals of Operations Research, Springer, vol. 316(1), pages 699-721, September.
    16. Bandekar, Shraddha Ramdas & Ghosh, Mini, 2022. "A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 1-31.
    17. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    18. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    19. Deborah Lacitignola & Fasma Diele & Carmela Marangi & Angela Monti & Teresa Serini & Simonetta Vernocchi, 2023. "Effects of Vitamin D Supplementation and Degradation on the Innate Immune System Response: Insights on SARS-CoV-2," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    20. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(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:matcom:v:219:y:2024:i:c:p:50-86. 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.