Skip to main content
SpringerLink
Log in

On the stochastic theory of compartments: The leaving process of the two-compartment systems

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system.

Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Cardenas, M. and J. H. Matis. 1974. “On the Stochastic Theory of Compartments: Solution forn-Compartment Systems with Irreversible, Time-dependent Transition Probabilities.”Bull. Math. Biol.,36, 489–504.

    Article  MATH  MathSciNet  Google Scholar 

  • — and J. H. Matis. 1975a. “On the Time-dependent Reversible Stochastic Compartmental Model—I. The General Two-compartment System.”Bull. Math. Biol. 37, 505–519.

    Article  MATH  MathSciNet  Google Scholar 

  • — and —. 1975b. “On the Time-dependent Reversible Stochastic Compartmental Model—II. A Class ofn-compartment Systems.”Bull. Math. Biol.,37, 555–564.

    Article  MATH  MathSciNet  Google Scholar 

  • Campello, L. and C. Cobelli, 1977. “Parameter Estimation of Biological Stochastic Compartmental Models. An Application.”IEEE Trans. Biomed. Engng, in press.

  • Chuang, S. and H. H. Lloyd. 1975. “Analysis and Identification of Stochastic Compartment Models in Pharmacokinetics: Implication for Cancer Chemotherapy.”Mathl Biosci.,22, 57–74.

    Article  MathSciNet  Google Scholar 

  • Cobelli, C. and L. M. Morato. 1978. “On the Identification by Filtering Techniques of a Biologicaln-compartment Model in which the Transport Rate Parameters are Assumed to be Stochastic Processes.”Bull. Math. Biol.,40, 651–660.

    Article  MATH  MathSciNet  Google Scholar 

  • Cox, D. R. 1962.Renewal Theory. London: Methuen.

    MATH  Google Scholar 

  • Gaver, D. F. 1963. “Random Hazard in Reliability Problems.”Technometrics,5, 211–216.

    Article  MathSciNet  Google Scholar 

  • Jacquez, J. A. 1972.Compartmental Analysis in Biology and Medicine. Amsterdam: Elsevier.

    Google Scholar 

  • Kodell, R. L. and J. H. Matis. 1976. “Estimating the Rate Constants in a Two-compartment Stochastic Model.”Biometrics,32, 377–380.

    Article  MATH  MathSciNet  Google Scholar 

  • Matis, J. H. and H. O. Hartley. 1971. “Stochastic Compartmental Analysis: Model and Least Squares Estimation from Time Series Data.”Biometrics,27, 77–102.

    Article  Google Scholar 

  • —, M. Cardenas and R. L. Kodell. 1974. “On the Probability of Reaching a Threshold in a Stochastic Mamillary System.”Bull. Math. Biol.,36, 445–454.

    Article  MATH  Google Scholar 

  • —, R. L. Kodell and M. Cardenas. 1976. “A Note on the Use of a Stochastic Mamillary Compartmental Model as an Environmental Safety Model.”Bull. Math. Biol.,38, 467–478.

    Article  MATH  Google Scholar 

  • Purdue, P. 1974a. “Stochastic Theory of Compartments.”Bull. Math. Biol.,36, 305–309.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1974b. “Stochastic Theory of Compartments: One and Two-compartment Systems.”Bull. Math. Biol.,36, 577–587.

    Article  MATH  MathSciNet  Google Scholar 

  • Serfoso, R. F. 1972. “Conditional Poisson Processes.”J. Appl. Prob.,9, 288–302.

    Article  Google Scholar 

  • Soong, I. I. 1971. “Pharmacokinetics with Uncertainties in Rate Constants.”Mathl Biosci.,12, 235–243.

    Article  Google Scholar 

  • —, 1972. “Pharmacokinetics with Uncertainties in Rate Constants—II. Sensitivity Analysis and Optimal Dosage Control.”Mathl Biosci.,13, 391–396.

    Article  MATH  Google Scholar 

  • — and J. W. Dowdee. 1974. “Pharmacokinetics with Uncertainties in Rate Constants—III. The Inverse Problem.”Mathl Biosci.,19, 343–353.

    Article  MATH  Google Scholar 

  • Thakur, A. K., A. Rescigno and D. Schafer. 1972. “On the Stochastic Theory of Compartments—I. A Single-compartment System.”Bull. Math. Biophys.,34, 53–63.

    MATH  MathSciNet  Google Scholar 

  • —— and —. 1973. “On the Stochastic Theory of Compartments—II. Multicompartment Systems.”Bull. Math. Biol.,35, 263–271.

    Article  MATH  MathSciNet  Google Scholar 

  • — and —. 1978. “On the Stochastic Theory of Compartments—III. General Time-dependent Reversible Systems.”Bull. Math. Biol.,40, 237–246.

    Article  MATH  Google Scholar 

  • Tolley, H. D., D. Burdick, K. G. Manton and E. Stallard. 1978. “A Compartment Model Approach to the Estimation of Tumor Incidence and Growth: Investigation of a Model of Cancer Latency.”Biometrics,34, 377–389.

    Article  Google Scholar 

  • Tsokos, J. O. and C. P. Tsokos, 1976. “Statistical Modeling of Pharmacokinetics Systems.” Trans. A.S.M.E., Ser. D;J. Dynam. Systems Measmt Control,98, 37–43.

    Article  Google Scholar 

  • Wiener, D. L. and P. Purdue. 1977. “The Stochastic Theory of Compartments—A Mamillary System.”Bull. Math. Biol.,39, 533–542.

    Article  Google Scholar 

  • Zelen, M. and M. Feinleib 1969. “On the Theory of Screening for Chronic Diseases.”Biometrika,56, 601–614.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistical Unit, University of Athens, Greece

    G. K. Agrafiotis

Authors
  1. G. K. Agrafiotis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agrafiotis, G.K. On the stochastic theory of compartments: The leaving process of the two-compartment systems. Bltn Mathcal Biology 43, 201–211 (1981). https://doi.org/10.1007/BF02459443

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02459443

Keywords

Search

Navigation