This study examined a single-compartment pharmacokinetic model with intravenous and oral administration. It investigated the trends in steady-state drug exposure and average steady-state plasma drug concentration under multiple dosing regimens. First, the combined drug administration model was a non-autonomous system, and we approximated the solution of the model by estimating the exact upper and lower bounds in conjunction with the comparison theorem for differential equations. We also demonstrated the existence, uniqueness, and stability of the solution. Second, we derived the steady-state drug exposure and compared it with the solution of the intravenous drug delivery model alone. The results indicate that the combined drug delivery scheme offers superior performance. Finally, we theoretically proved the change rule of average steady-state blood drug concentration under different dosing regimens, and verified its feasibility and rationality by combining the numerical simulation results of Phenytoin sodium.

This paper investigated the dynamical behaviors of the SIQS (susceptible, infected, isolated, and again susceptible) infectious disease model with nonlinear incidence rate and degenerate diffusion in a stochastic environment. By introducing nonlinear contagion rate, the model was able to more realistically reflect the complexity of real-world disease transmission, including the effects of social behavior, medical resource constraints, and public health interventions. It was proved that the infectious disease will be extinct when $R_0^s<1$. Furthermore, by utilizing Markov semigroup theory, we obtained that there existed stationary distribution for the system when $R_0^s>1$. Numerical simulations were conducted by introducing three different forms of nonlinear incidence rates (standard incidence, non-monotonic incidence, Beddington-DeAngelis incidence) to verify our results.