Threshold dynamics of a predator–prey model with age-structured prey

• Main Authors: Yang Lu, Shengqiang Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: Advances in Difference Equations
• Subjects: Predator–prey model; Age structured; Persistence; Delay integro-differential equations
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1614-y

Abstract A predator–prey model, with aged structure in the prey population and the assumption that the predator hunts prey of all ages, is proposed and investigated. Using the uniform persistence theory for infinite dimensional dynamical systems, the global threshold dynamics of the model determined by the predator’s net reproductive number ℜP $\Re_{P}$ are established: the predator-free equilibrium is globally stable if ℜP<1 $\Re_{P}<1$, while the predator persists if ℜP>1 $\Re_{P}>1$. Numerical simulations are given to illustrate the results.