Predator-Prey Interactions, Age Structures and Delay Equations

TL;DR

This paper introduces a general age-structured predator-prey model that reduces complex PDEs to delay differential equations, enabling more accurate and physically consistent analysis of predator-prey dynamics with delays.

Contribution

It develops a novel framework for age-structured predator-prey systems, transforming PDEs into delay differential equations for improved modeling accuracy.

Findings

Reduction of PDEs to delay differential equations with one or two delays

Analysis of existing models within the new framework

Presentation of a delay Rosenzweig-MacArthur predator-prey model

Abstract

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.