Mathematical analysis of nonlinear combination drug delivery

Jiali Shi; Zhongyi Xiang; Jiali Shi; Zhongyi Xiang

doi:10.3934/era.2025082

Electronic Research Archive

2025, Volume 33, Issue 3: 1812-1835. doi: 10.3934/era.2025082

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Research article

Mathematical analysis of nonlinear combination drug delivery

Jiali Shi ,
Zhongyi Xiang ^,

School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China

Received: 19 January 2025 Revised: 13 March 2025 Accepted: 20 March 2025 Published: 28 March 2025

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.
- pharmacokinetic model,
- combined drug administration,
- steady-state drug exposure,
- average steady-state concentration
Citation: Jiali Shi, Zhongyi Xiang. Mathematical analysis of nonlinear combination drug delivery[J]. Electronic Research Archive, 2025, 33(3): 1812-1835. doi: 10.3934/era.2025082

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Abstract

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.

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