Nonlinear Birth-Immigration-Death Models
Consider now adding immigration at rateIto the nonlinear birth-death model. This new model is more realistic biologically in many applications, including the AHB and muskrat problems, however it is largely ignored in the literature. Perhaps there are two reasons for this. One is that the deterministic models become more unwieldy whenIis included. The other reason is that inclusion of biologically reasonable levels ofIseldom have a large impact on the qualitativeshapeof the deterministic solution. Consequently, in practice a statistical analysis would often fail to show that the inclusion of the parameter leads to a substantial improvement in the goodness-of-fit of the model to the data. In short, though there are often compelling biological reasons to include immigration, it is usually excluded from the model because it complicates thedeterministicmodel and because its inclusion is typically not statistically “significant”.
KeywordsEquilibrium Distribution Deterministic Model Kolmogorov Equation Deterministic Solution Saddlepoint Approximation
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