TY - JOUR
T1 - Convergence dynamics in one eco-epidemiological model
T2 - Self-healing and some related results
AU - Krishchenko, Alexander P.
AU - Starkov, Konstantin E.
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/6
Y1 - 2020/6
N2 - 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.
AB - 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.
KW - Convergence dynamics
KW - Eco-epidemiological model
KW - Extinction
KW - Localization method
UR - http://www.scopus.com/inward/record.url?scp=85079842765&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2020.105223
DO - 10.1016/j.cnsns.2020.105223
M3 - Artículo
AN - SCOPUS:85079842765
SN - 1007-5704
VL - 85
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 105223
ER -