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Stochastic compartmental model with branching particles

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Abstract

A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.

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Literature

  • Athreya, K. B. and P. E. Ney. 1972.Branching Processes. Berlin: Springer.

    Google Scholar 

  • Coddington, E. A. and N. Levinson. 1965.Theory of Ordinary Differential Equations. New York: McGraw-Hill.

    Google Scholar 

  • Faddy, M. J. (1976). “A Note on the General Time-Dependent Stochastic Compartmental Model.”Biometrics 32, 443–448.

    Article  MATH  MathSciNet  Google Scholar 

  • Harris, T. E. (1963)The Theory of Branching Processes. Berlin: Springer.

    Google Scholar 

  • Iosifescu, M. and P. Tãuto. (1973).Stochastic Processes and Applications in Biology and Medicine, Vol. 2. Berlin: Springer.

    Google Scholar 

  • Jagers, P. (1975).Branching Processes with Biological Applications. New York: John Wiley.

    Google Scholar 

  • Karlin, S. (1966).A First Course in Stochastic Processes. New York: Academic Press.

    Google Scholar 

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

    Article  Google Scholar 

  • —. (1972). “Gamma Time Dependence on Blaxter's Compartmental Model.”Biometrics 28, 597–602.

    Article  Google Scholar 

  • Purdue, P. (1979). “Stochastic Compartmental Models: a Review of the Mathematical Theory With Ecological Applications.” InCompartmental Analysis of Ecosystem Models, Ed. J. H. Matis, B. C. Patten and G. C. White. Burtonville, MD: International Co-operative.

    Google Scholar 

  • Puri, P. S. (1968). “Interconnected Birth and Death Processes.”J. Appl. Prob. 5, 334–349.

    Article  MATH  MathSciNet  Google Scholar 

  • Raman, S. and C. L. Chiang. (1973). “On a Solution of the Migration Process and the Application to a Problem in Epidemiology.”J. Appl. Prob. 10, 718–727.

    Article  MATH  MathSciNet  Google Scholar 

  • Renshaw, E. (1972). “Birth, Death and Migration Processes.”Biometrika 59, 49–60.

    Article  MATH  MathSciNet  Google Scholar 

  • — (1973). “Interconnected Population Processes.”J. Appl. Prob. 10, 1–14.

    Article  MATH  MathSciNet  Google Scholar 

  • Rescigno, A. and J. S. Beck. (1972). “Compartments.” InFoundations of Mathematical Biology, Ed. Robert Rosen. New York: Academic Press.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, 600 036, Madras, India

    P. R. Parthasarathy & P. Mayilswami

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  1. P. R. Parthasarathy
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  2. P. Mayilswami
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Parthasarathy, P.R., Mayilswami, P. Stochastic compartmental model with branching particles. Bltn Mathcal Biology 43, 347–360 (1981). https://doi.org/10.1007/BF02462205

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  • DOI: https://doi.org/10.1007/BF02462205

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