Abstract
In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
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Literature
Bernard, S. R. 1977. “An Urn Model Study of Variability within a Compartment.”Bull. Math. Biol.,39, 463–470.
Feller, W. 1971.An Introduction to Probability Theory and its Applications, Vol. II. new York: John Wiley and Sons.
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. Biology,41, 491–515.
— and T. E. Wehrly. 1979a. “An Approach to a Compartmental Model with Multiple Sources of Stochasticity for Modeling Ecological Systems.” InCompartmental Analysis of Ecosystem Models, Ed. J. H. Matis, B. C. Patten and G. C. White, pp. 195–222. Maryland, International Co-operative Publishing House.
—. 1979b. “Stochastic Models of Compartmental Systems.”Biometrics,35, 199–220.
Purdue, P. 1979. “Stochastic Compartmental Models: a Review of the Mathematical Theory with Ecological Applications”. In:Compartmental Analysis of Ecosystem Models, Ed. J. H. Matis, B. C. Patten and G. C. White, pp. 223–260. Maryland: International Cooperative Publishing House.
Uppuluri, V. R. R. and K. Anderson. 1976. “A Polya Urn Scheme.” Unpublished note.
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Purdue, P. Variability in a single compartment system: A note on S. R. Bernard's model. Bltn Mathcal Biology 43, 111–116 (1981). https://doi.org/10.1007/BF02460944
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DOI: https://doi.org/10.1007/BF02460944