Advertisement

Bulletin of Mathematical Biology

, Volume 43, Issue 4, pp 503–512 | Cite as

A one-compartment model with stochastic parameter

  • Karmeshu
  • C. K. Gupta
Article

Abstract

We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.

Keywords

Transfer Rate Coloured Noise Stochastic Parameter Compartmental System Moment Sense 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Bourret, R. C., U. Frisch and A. Pouquet. 1973. “Brownian Motion of Harmonic Oscillation with Stochastic Frequency.”Physica 65, 303–320.CrossRefGoogle Scholar
  2. Campello, L. and C. Cobelli. 1978. “Parameter Estimation of Biological Stochastic Compartmental Models. An Application.”IEEE Trans. Biomed. Engng. BME 25, 139–146.Google Scholar
  3. 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.MATHMathSciNetCrossRefGoogle Scholar
  4. — and-—. 1975. “On the Time-Dependent Reversible Stochastic Compartmental Model—I. The General Two-Compartment Systems.”Bull. Math. Biol. 37, 505–519.MATHMathSciNetCrossRefGoogle Scholar
  5. Cobelli, C. and L. M. Morat. 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.MATHMathSciNetCrossRefGoogle Scholar
  6. Faddy, M. J. 1976. “A Note on the General Time Dependent Stochastic Compartmental Model.”Biometrics 32, 443–448.MATHMathSciNetCrossRefGoogle Scholar
  7. Gibaldi, M. and D. Perrier. 1975.Pharmacokinetics. New York: Dekker.Google Scholar
  8. Hoel, P. G. 1954.Introduction to Mathematical Statistics. New York: Wiley.MATHGoogle Scholar
  9. Jacquez, J. A. 1972.Compartmental Analysis in Biology and Medicine. New York: Elsevier.Google Scholar
  10. Kapadia, A. S. and B. C. McInnis. 1976. “A Stochastic Compartment Model with Continuous Infusion.”Bull. Math. Biol. 38, 695–700.MATHMathSciNetGoogle Scholar
  11. Kitahara, K., W. Horsethemke and R. Lefever. 1979. “Coloured Noise Induced Transitions.”Phys. Lett. 70A, 377–380.Google Scholar
  12. Matis, J. H. and H. D. Tolley. 1979. “Compartmental Models with Multiple Sources of Stochastic Variability: the One-Compartment, Time-Invariant, Hazard Rate Case.”Bull. Math. Biol. 41, 491–515.MATHMathSciNetGoogle Scholar
  13. Soong, T. T. 1971. “Pharmacokinetics with Uncertainties in Rate Constants.”Mathl. Biosci. 12, 235–243.CrossRefGoogle Scholar
  14. Tsokos, J. O. and C. P. Tsokos. 1976. “Statistical Modelling of Pharmacokinetics Systems.”J. Dynam. Systems Measmt. Control 98, 37–43.CrossRefGoogle Scholar
  15. Waldo, D. R., L. W. Smith and E. L. Cox. 1972. “Model of Cellulose Disappearance from the Rumen.”J. Dairy Sci. 55, 125–129.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1981

Authors and Affiliations

  • Karmeshu
    • 1
  • C. K. Gupta
    • 2
  1. 1.Department of PhysicsUniversity of WaterlooWaterlooCanada
  2. 2.V.P. Chest InstituteUniversity of DelhiDelhiIndia

Personalised recommendations