Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T00:49:37.651Z Has data issue: false hasContentIssue false
  • English
  • Français

A Laplace transform approach to direct and inverse problems for multi-compartment models

Part of: General theory in ordinary differential equations Algebraic combinatorics Integral transforms, operational calculus Physiological, cellular and medical topics

Published online by Cambridge University Press:  16 March 2022

M. RODRIGO
M. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Multi-compartment models described by systems of linear ordinary differential equations are considered. Catenary models are a particular class where the compartments are arranged in a chain. A unified methodology based on the Laplace transform is utilised to solve direct and inverse problems for multi-compartment models. Explicit formulas for the parameters in a catenary model are obtained in terms of the roots of elementary symmetric polynomials. A method to estimate parameters for a general multi-compartment model is also provided. Results of numerical simulations are presented to illustrate the effectiveness of the approach.

Keywords

Compartment modelinverse problemLaplace transformpharmacokinetics

MSC classification

Primary: 92C42: Systems biology, networks 34A55: Inverse problems 44A10: Laplace transform
Secondary: 05E05: Symmetric functions and generalizations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 6 , December 2022 , pp. 1170 - 1184
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D. H. (1983) Compartmental Modeling and Tracer Kinetics . Lecture Notes in Biomathematics, Vol. 50, Springer-Verlag, Berlin.Google Scholar
Godfrey, K. (1983) Compartmental Models and Their Application, Academic Press, London.Google Scholar
Holder, A. B. & Rodrigo, M. R. (2013) An integration-based method for estimating parameters in a system of differential equations. Appl. Math. Comput. 219(18), 9700–9708.Google Scholar
Li, T. R. & Rodrigo, M. R. (2017) Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms. Eur. J. Appl. Math. 28(5), 789–826.CrossRefGoogle Scholar
Macdonald, I. G. (1979) Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs, Clarendon Press, Oxford.Google Scholar
Putzer, E. J. (1966) Avoiding the Jordan canonical form in the discussion of linear systems with constant coefficients. Am. Math. Mon. 73(1), 2–7.CrossRefGoogle Scholar
Rodrigo, M. R. & Mamon, R. S. (2007) Recovery of time-dependent parameters of a Black-Scholes-type equation: an inverse Stieltjes moment technique. J. Appl. Math. 2007, Article ID 62098, doi: 10.1155/2007/62098.CrossRefGoogle Scholar
Rodrigo, M. R. & Mamon, R. S. (2014) An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions. Quant. Financ. 14(11), 1961–1970.CrossRefGoogle Scholar
Rodrigo, M. R. (2015) Time of death estimation from temperature readings only: a Laplace transform approach. Appl. Math. Lett. 39, 47–52.CrossRefGoogle Scholar
Rodrigo, M. R. (2020) On a generalisation of the fundamental matrix and the solution of operator equations. Int. J. Appl. Math. 33(3), 413–438.CrossRefGoogle Scholar
Xi, X., Rodrigo, M. R. & Mamon, R. S. (2012) Parameter estimation of a regime-switching model using an inverse Stieltjes moment approach. In: Cohen, S., Madan, D., Siu, T. K. and Yang, H. (editors), Advances in Statistics, Probability and Actuarial Science - Festschrift Volume in Honour of Robert Elliott’s 70th Birthday, World Scientific, Singapore, pp. 549–568.Google Scholar
Walter, G. G. & Contreras, M. (1999) Compartmental Modeling with Networks, Birkhäuser, Boston.CrossRefGoogle Scholar
Zulkarnaen, D. & Rodrigo, M. R. (2020) Modelling human carrying capacity as a function of food availability. ANZIAM J. 62, 318–333.CrossRefGoogle Scholar