Mathematical Modeling for Contagious Dental Health Issue: An Early Study of Streptococcus mutans Transmission

Dental caries is an example of an oral infectious disease that affects many people worldwide, but it is not well studied in deterministic mathematical modeling. Therefore, we are interested in studying the dynamics of tooth cavity disease using a deterministic modeling approach. We propose a delay differential equation system (DDEs) to describe the phenomenon. The breakthrough of the constructed model is the formulation of the recovery rate as a saturation function constrained by healthcare capacity and the plausibility of caries reformation. In addition, we consider two controls, such as a health campaign and a post-treatment intervention. The mathematical analysis yields equilibrium solutions and their stability, which is determined by the basic reproduction number R0. Furthermore, backward bifurcation occurs as the medical facility’s capacity decreases, driven by an increasing infectious population. The sensitivity analysis results indicate that both considered controls are the most influential parameters. The optimal control problem is formulated using the Pontryagin Maximum Principle to obtain an optimal solution in suppressing the number of caries formation cases. At the end, a numerical simulation shows that interventions reduce the risk of transmission and suppress the number of infectious individuals. The constructed model has excellent future potential, such as generating a function for relapse cases or other preventive actions into an optimal control problem.