A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population. (August 2022)

• Record Type: Journal Article
• Authors: Kumar, Pushpendra; Govindaraj, V.; Erturk, Vedat Suat
• Is Part Of: Chaos, solitons and fractals. Volume 161(2022)
• Publication Date: 2022-08
• Subjects: 26A33 -- 65D30 -- 92D25 -- 93A30; Teeth/tooth -- Cavity -- Mathematical model -- Caputo fractional derivative -- Existence and stability -- The predictor-corrector scheme; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112370
• Languages: English
• ISSNs: 0960-0779

Abstract

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.