The Basic Approach to Age-Structured Population Dynamics by Mimmo Iannelli & Fabio Milner

Author:Mimmo Iannelli & Fabio Milner
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

(5.36)

with the following mathematical assumptions on the rates (5.36)2

(5.37)

where we have set

(5.38)

Thus the model reads

(5.39)

Under the constitutive assumptions above, all the basic hypotheses are satisfied and the results proved in the previous sections hold. Concerning the existence of steady states, the net reproduction number at a constant weighted size x has the form

(5.40)

We see from condition (5.37, i) that the parameter R 0 is actually the intrinsic net reproduction number , that is the net reproduction number at weighted size x = 0, when the logistic effect is not active. Since we have a single weighted size S, the system (5.32) reduces to the single equation

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