A study of a new mathematical model on progression and control of dental caries through wavelet analysis

Dental caries remains one of the most prevalent oral health problems worldwide, making it essential to understand the dynamic processes that drive tooth decay progression and recovery. In the history of mathematical modeling, several diseases in humans, plants, and animals have been studied using modeling theory. In this study, we propose a mathematical model to investigate the transmission and control of tooth decay using five epidemiological compartments: susceptible teeth, exposed teeth, decayed teeth, treated teeth, and recovered teeth formed of assuming different parameters, such as the rate of exposed teeth, the rate of fluoride deficiency, the rate of decay, rate of dry mouth, etc., The model captures the natural course of dental deterioration, from initial susceptibility and exposure to decay and subsequent intervention through treatment or natural recovery. Legendre wavelet method (LWM) and other numerical techniques are employed to study the efficiency, nature of five different variables, and how they behave concerning the change of the independent variable (ζ). Numerical simulations are also compared with different methods to make the results obtained more accurate with RK4, LWM, and NDSolve. The numerical tables are presented for numerical values, and graphical illustrations demonstrate the nature of the five dependent variables. This framework provides a theoretical and numerical foundation for guiding oral health policies and supporting educational campaigns to minimize tooth decay progression within populations.