Modeling and numerical analysis of saturation incidence and saturated treatment of dental caries infection

Abstrakt

Dental caries are holes in teeth that form when acid in the mouth erodes tooth enamel. In this study, a SEIR model of dental caries infection is constructed with saturation incidence rate and  saturated treatment function and we analyze the numerical behavior of the basic reproduction number and stability. Non-standard finite differences (NSFD) scheme was constructed for the SEIR model of dental caries infection and were compared with the Runge Kutta fourth order (RK-4) scheme and Forward Euler (FD) scheme. The NSFD scheme preserves positivity property and also proved to be an effective and efficient scheme for numerical solution of epidemic models. The dental caries (delay) free equilibrium and endemic equilibrium were obtained. Results of the numerical testing reveals that RK-4 scheme and forward Euler (FD) scheme is conditionally convergent and may loss some important properties of continuous system for certain values of step size h. Also, the numerical result further discloses that if
medical resources are maximized and treatment not delayed, dental caries infection dynamics will decrease with transient time and the infection will eventually be eradicated from the population.