In this paper we study the phenomena of the extinction and persistence of predator populations of the three-dimensional Kooi et al. model in the global formulation of the problem. This model contains three populations: prey, susceptible predators and infected predators. We compute ultimate sizes of interacting populations and establish that all biologically feasible trajectories eventually enter in some bounded domain and remain there. We derive analytical conditions for the extinction of the infected predator population in cases of different/equal mortality rates of predators. In particular, we find conditions under which 1) the population of prey persists, while both of predator populations die out, 2) the populations of prey and susceptible predators persist, while the population of infected predators dies out. Besides, we describe the case when at least one periodic orbit exists in the disease-free invariant plane. Our analysis is based on using the localization method of compact invariant sets and the theorem of LaSalle. Main theoretical results are illustrated by numerical simulation.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|State||Published - Jun 2020|
- Convergence dynamics
- Eco-epidemiological model
- Localization method