Similarity transformation approach to identifiability analysis of nonlinear compartmental models.

Abstract:

:Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Vajda S,Godfrey KR,Rabitz H

doi

10.1016/0025-5564(89)90024-2

subject

Has Abstract

pub_date

1989-04-01 00:00:00

pages

217-48

issue

2

eissn

0025-5564

issn

1879-3134

pii

0025-5564(89)90024-2

journal_volume

93

pub_type

杂志文章
  • Optimal foraging by zooplankton within patches: the case of Daphnia.

    abstract::The motions of many physical particles as well as living creatures are mediated by random influences or 'noise'. One might expect that over evolutionary time scales internal random processes found in living systems display characteristics that maximize fitness. Here we focus on animal random search strategies [G.M. Vi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.11.014

    authors: Garcia R,Moss F,Nihongi A,Strickler JR,Göller S,Erdmann U,Schimansky-Geier L,Sokolov IM

    更新日期:2007-06-01 00:00:00

  • Four-state models and regulation of contraction of smooth muscle. I. Physical considerations, stability, and solutions.

    abstract::Cyclic four-state models are frequently used in biology to represent a variety of molecular behaviors. A common experimental strategy to test such models is to follow the behavior of the real system after some of the rate constants are changed in a stepwise manner. We analyze the mathematical behavior of a simple exam...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90086-c

    authors: Lazalde CA,Barr L

    更新日期:1992-11-01 00:00:00

  • Metabolic isotopomer labeling systems. Part III: path tracing.

    abstract::Isotope labeling systems (ILSs) are sets of balance equations that quantitatively describe the distribution of isotopic tracers in metabolic networks. The solution of ILSs, i.e., the calculation of isotopic labeling distributions (mostly in steady state) is the fundamental computational step of (13)C metabolic flux an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2013.02.012

    authors: Wiechert W,Nöh K,Weitzel M

    更新日期:2013-07-01 00:00:00

  • Heterogeneity in dynamic species abundance models: the selective effect of extinction processes.

    abstract::There is often large variation in traits across the species of a community. In particular, variation in life history traits affecting population dynamics is likely to affect the species abundance distribution. Applying a dynamic and heterogeneous species abundance model we study how differences in extinction time for ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2007.06.002

    authors: Engen S

    更新日期:2007-12-01 00:00:00

  • Scaffold-mediated nucleation of protein signaling complexes: elementary principles.

    abstract::Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleati...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2011.06.003

    authors: Yang J,Hlavacek WS

    更新日期:2011-08-01 00:00:00

  • On using Lehmann alternatives with nonresponders.

    abstract::The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of respon...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90052-x

    authors: Razzaghi M,Nanthakumar A

    更新日期:1992-04-01 00:00:00

  • Subthreshold and superthreshold coexistence of pathogen variants: the impact of host age-structure.

    abstract::It is well known that in the most general epidemic models with multiple pathogen variants a competitive exclusion principle is valid, such that the variant with the highest reproduction number eliminates the rest. Mechanisms such as super-infection, coinfection, and cross-immunity can lead to pathogen polymorphism whe...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.09.010

    authors: Martcheva M,Pilyugin SS,Holt RD

    更新日期:2007-05-01 00:00:00

  • Exploration of sexual dimorphism and inter-individual variability in multivariate parameter spaces for a pharmacokinetic compartment model.

    abstract::Pharmacokinetic models are particularly useful to study the underlying and complex physiological mechanisms contributing to clinical differences across patient subgroups or special populations. Unfortunately, the inherent variability of biological systems and knowledge gaps in physiological data limit confidence in mo...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.12.011

    authors: Scherholz ML,Androulakis IP

    更新日期:2019-02-01 00:00:00

  • On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model.

    abstract::A Gompertz-type diffusion process characterized by the presence of exogenous factors in the drift term is considered. Such a process is able to describe the dynamics of populations in which both the intrinsic rates are modified by means of time-dependent terms. In order to quantify the effect of such terms the evaluat...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2013.01.001

    authors: Albano G,Giorno V,Román-Román P,Torres-Ruiz F

    更新日期:2013-09-01 00:00:00

  • Closed-loop stability of pharmacokinetic-pharmacodynamic models.

    abstract::In automatic feedback control of intravenous drug infusions, convergence to the setpoint is an important objective. This paper examines the stability of pharmacokinetic-pharmacodynamic models of patient response regulated with proportional integral feedback. The model consists of three components: linear compartmental...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(97)00076-x

    authors: Wada DR

    更新日期:1997-12-01 00:00:00

  • Evaluating spread of invaders from gravity scores--a way of using gravity models in ecology.

    abstract::This study is a theoretical excursion into gravity models and their usability in evaluating importance of spatial structure and population development for the spread of colonizing organisms. A so called "gravity score" for sites is deduced, and such a score could be used for predicting risk of colonization once one si...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2009.08.008

    authors: Järemo J

    更新日期:2009-11-01 00:00:00

  • A model of HIV/AIDS with staged progression and amelioration.

    abstract::An epidemic model with multiple stages of infection is studied. The model allows for infected individuals to move from advanced stages of infection back to less advanced stages of infection. A threshold parameter which determines the local stability of the disease free equilibrium is found and interpreted. Under condi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00149-9

    authors: McCluskey CC

    更新日期:2003-01-01 00:00:00

  • Spectra-based estimates of certain time-domain parameters of a bivariate stationary-point process.

    abstract::We consider estimates of certain time-domain parameters of a bivariate stationary-point process based on modified periodogram statistics. These estimates are shown to be asymptotically normal under regularity conditions. In the computations of the estimates, the advantage of using the FFT algorithm is demonstrated. Th...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(91)90061-m

    authors: Rigas AG

    更新日期:1991-05-01 00:00:00

  • Dependence of mating rate on variance of eclosion time of cicadas (cicadidae).

    abstract::In many cicadas, a phenomenon is observed in which the peak of emergence of males precedes that of females (protandry). Generally, it is known that the ecology of emergence of insects is closely related to mating, and protandry is said to be the strategy of males to eclose early and to attempt mating with virgin femal...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.08.006

    authors: Saisho Y

    更新日期:2018-11-01 00:00:00

  • On global and local critical points of extended contact process on homogeneous trees.

    abstract::We study spatial stochastic epidemic models called households models. The households models have more than two states at each vertex of a graph in contrast to the contact process. We show that, in the households models on trees, two thresholds of infection rates characterize epidemics. The global critical infection ra...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2008.02.004

    authors: Sugimine N,Masuda N,Konno N,Aihara K

    更新日期:2008-05-01 00:00:00

  • Threshold parameters for epidemics in different community settings.

    abstract::Threshold parameters of epidemic models play a central role in the assessment of proposed control strategies for infectious diseases. They have been determined for numerous standard epidemic models. This paper points out, with several examples, that threshold parameters depend on the social setting of the community an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(94)00061-4

    authors: Becker NG,Bahrampour A,Dietz K

    更新日期:1995-10-01 00:00:00

  • Some remarks on definition and validity of terms used in models for infectious disease spread.

    abstract::The epidemiology of infectious diseases makes use of a number of terms, such as exposure, infected, carrier, attack rate, and immunity. Researchers who intend to model the spread of epidemics should be aware of the problems with some of these terms. The role played by inapparent, or subclinical, infections is receivin...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(91)90001-y

    authors: Giesecke J

    更新日期:1991-12-01 00:00:00

  • Multiscale modelling of saliva secretion.

    abstract::We review a multiscale model of saliva secretion, describing in brief how the model is constructed and what we have so far learned from it. The model begins at the level of inositol trisphosphate receptors (IPR), and proceeds through the cellular level (with a model of acinar cell calcium dynamics) to the multicellula...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2014.06.017

    authors: Sneyd J,Crampin E,Yule D

    更新日期:2014-11-01 00:00:00

  • A class of phylogenetic networks reconstructable from ancestral profiles.

    abstract::Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set X of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, hybrid evolution, endosymbiosis, and lateral gene transfer). A...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2019.04.009

    authors: Erdős PL,Semple C,Steel M

    更新日期:2019-07-01 00:00:00

  • Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

    abstract::When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find threshol...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(01)00093-1

    authors: Gallop RJ,Mode CJ,Sleeman CK

    更新日期:2002-05-01 00:00:00

  • Global stability for a 2n+1 dimensional HIV/AIDS epidemic model with treatments.

    abstract::In this work, we derive and analyze a 2n+1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treat...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.03.013

    authors: Otunuga OM

    更新日期:2018-05-01 00:00:00

  • Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model.

    abstract::Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume t...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.07.001

    authors: Marquis AD,Arnold A,Dean-Bernhoft C,Carlson BE,Olufsen MS

    更新日期:2018-10-01 00:00:00

  • A nonlinear numerical model of percutaneous drug absorption.

    abstract::A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90054-z

    authors: Kubota K,Twizell EH

    更新日期:1992-03-01 00:00:00

  • Mean and quasideterministic equivalence for linear stochastic dynamics.

    abstract::In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, wi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(89)90010-2

    authors: Hanson FB,Ryan D

    更新日期:1989-03-01 00:00:00

  • Partial identification of underdetermined compartmental models: a method based on positive linear Lyapunov functions.

    abstract::A class of models is considered in which the number of unknown parameters exceeds the number of independent equations that are derived from the input/observation configuration. It is shown that, under certain circumstances, if the number of unknown parameters is sufficiently decreased by setting some of the exit param...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(95)00049-6

    authors: Eisenfeld J

    更新日期:1996-03-01 00:00:00

  • In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons.

    abstract::We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation tim...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2013.02.007

    authors: Ao X,Hänggi P,Schmid G

    更新日期:2013-09-01 00:00:00

  • CXCR4 and CCR5 regulation and expression patterns on T- and monocyte-macrophage cell lineages: implications for susceptibility to infection by HIV-1.

    abstract::Chemokine receptor expression may vary dramatically among cell subsets. Therefore, the stage of differentiation and the lineage of CD4 cells may profoundly affect their susceptibility to infection by human immunodeficiency virus type 1 (HIV-1). However, the mechanisms of coreceptor competition for association with HIV...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2005.01.002

    authors: Joly M,Pinto JM

    更新日期:2005-05-01 00:00:00

  • Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

    abstract::This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to pred...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2017.08.009

    authors: Kumar D,Kumar P,Rai KN

    更新日期:2017-11-01 00:00:00

  • Theory of the locomotion of nematodes: control of the somatic motor neurons by interneurons.

    abstract::The only animal of which the complete neural circuitry is known at the submicroscopical level is the nematode Caenorhabditis elegans. This anatomical knowledge is complemented by functional insight from electrophysiological experiments in the related nematode Ascaris lumbricoides, which show that Ascaris motor neurons...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(93)90033-7

    authors: Niebur E,Erdös P

    更新日期:1993-11-01 00:00:00

  • Closure operations in phylogenetics.

    abstract::Closure operations are a useful device in both the theory and practice of tree reconstruction in biology and other areas of classification. These operations take a collection of trees (rooted or unrooted) that classify overlapping sets of objects at their leaves, and infer further tree-like relationships. In this pape...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.11.005

    authors: Grünewald S,Steel M,Swenson MS

    更新日期:2007-08-01 00:00:00