| Contents |
| In the context of population dynamics, DDEs with constant delay can be obtained, e.g., from the
balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant. The delay arises naturally from biology as the age-at-maturity of individuals.
A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential equations is reduced to a system of (neutral) delay differential equations with one or two delays. Thanks to this approach, physically
correct models for predator-prey with delay are provided. Previous models are considered and
analysed in view of the above results. A Rosenzweig-MacArthur model with delay is presented
as an example.
The basic model is finally extended to obtain a predator-prey model with SIS dynamics and delay. |
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