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- Title
Real Branches and Stability of a New Transcendental Function Arising in Pharmacokinetic Modeling.
- Authors
Wu, Xiaotian; Zhang, Hao; Li, Jun
- Abstract
This study aims to investigate the morphism and stability of a family of new transcendental functions, namely H functions, which have been proven a suitable vehicle for expressing the exact solutions of drug concentration over time of a one-compartment pharmacokinetic (PK) model with sigmoidal Hill elimination. Restricting in the real values of Hill coefficients α for the H functions, the real branches of the H functions are identified and their stabilities are analyzed. The number, shape, monotonicity, and concavity of all real branches are determined, as well as the stability of each branch when α is changed. The results show that the principal real branch H 0 (s) is the unique stable branch for α ∈ R , while other real branches can only exist for α ∈ Q and classified therein. A numerical experiment is conducted between the proposed H function and other commonly used solvers, including differential equation solvers (ode45), and the results indicate that the former is more reliable and has an acceptable level of induced error.
- Subjects
PHARMACOKINETICS; FAMILY stability; DIFFERENTIAL equations; TRANSCENDENTAL functions
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2024, Vol 47, Issue 2, p1
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-023-01630-y