Linear Immigration-Death Models
Part of the Lecture Notes in Statistics book series (LNS, volume 145)
Consider first modeling a single population of sizeX(t)with the linear death rate
and immigration rate I. This very simple case of the general rates in (3.40) extends the illustration in Chapter 3 by relaxing the assumption of an initial population size zero. The model, as previously noted, is called the linear immigration-death (LID) model, and it is widely used as the standard stochastic one-compartmental model. This model is developed thoroughly in  in a compartmental context. A simple application developed subsequently is modeling the bioaccumulation of mercury, described in Section 2.4. We have also used the model extensively to describe the passage of digesta in ruminant animals, see e.g. [15, 16, 59].
$$ \mu x = aX $$
KeywordsDeterministic Model Moment Generate Function Immigration Rate Kolmogorov Equation Saddlepoint Approximation
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© Springer-Verlag New York, Inc. 2000