Exploring the dynamics of bacterial growth in oral biofilm causing dental caries: A study of deterministic modeling

Dental caries is a health issue characterized by the attachment of an oral biofilm that contains bacteria to tooth surface. At present, several deterministic models have been constructed to explore numerous phenomena related to population dynamics. Despite the existing models, only two pieces of literature have explored bacterial growth in oral biofilms using ordinary differential equations with a deterministic modeling approach. Therefore, this study aims to propose a deterministic model to assess the dynamics of bacterial growth in oral biofilms, considering the interaction between the microorganisms. The model focuses on 3 bacteria, namely Streptococcus mutans (S. mutans), Streptococcus sanguinis (S. sanguinis), and Veillonella spp. A mathematical assessment was performed to ensure that the obtained solutions were feasible for biological discussion. Subsequently, the ratio of S. mutans against S. sanguinis under the equilibrium was formulated as the threshold to measure the risk level of caries formation. Additionally, a sensitivity analysis was also performed to appraise the parameters' influence on the observed dynamics. The results showed that there was a positive correlation between the presence of Veillonella spp. and an increased risk of caries formation. The theory of optimal control was used to investigate the optimal scenario for intervening in the threshold ratio by considering the effect of antibacterial utilization. Lastly, a numerical simulation was conducted to confirm the analysis results and scrutinize each bacterial dynamics under several scenarios represented by the selected parameter with varied values.