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A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population

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  • Kumar, Pushpendra
  • Govindaraj, V.
  • Erturk, Vedat Suat

Abstract

In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.

Suggested Citation

  • Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s096007792200580x
    DOI: 10.1016/j.chaos.2022.112370
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    References listed on IDEAS

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    1. Nabi, Khondoker Nazmoon & Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Projections and fractional dynamics of COVID-19 with optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    6. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    Cited by:

    1. Sanubari Tansah Tresna & Nursanti Anggriani & Herlina Napitupulu & Wan Muhamad Amir W. Ahmad, 2024. "Deterministic Modeling of the Issue of Dental Caries and Oral Bacterial Growth: A Brief Review," Mathematics, MDPI, vol. 12(14), pages 1-14, July.

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