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Dynamics of a ratio-dependent eco-epidemiological system with prey harvesting. (English) Zbl 1198.34077

Authors’ abstract: We study a ratio-dependent eco-epidemiological system where the prey population is subjected to harvesting. Mathematical results like positive invariance, boundedness, stability of equilibria, and permanence of the system are established. The dynamics of zero equilibria are thoroughly investigated to find conditions on the system parameters such that trajectories starting from the domain of interest can reach a zero equilibrium following any fixed direction. We also study suitable conditions for non-existence of a periodic solution around the interior equilibrium. Computer simulations are carried out to illustrate different analytical findings.

Reviewer’s remark: A related paper is: Z. Zhang and Z. Hou, Nonlinear Anal., Real World Appl. 11, No. 3, 1560–1571 (2010; Zbl 1198.34081).


MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
34C05Location of integral curves, singular points, limit cycles (ODE)
92D30Epidemiology
92D40Ecology
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