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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:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D30 Epidemiology
92D40 Ecology
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