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On an eco-epidemiological model with prey harvesting and predator switching: local and global perspectives. (English) Zbl 1205.34048
Summary: We study an eco-epidemiological model where the prey disease is modeled by a Susceptible-Infected (SI) scheme. Saturation incidence kinetics is used to model the contact process. The predator population switches among susceptible and infected prey. The prey species is supposed to be commercially viable and undergo constant non-selective harvesting. We study the stability aspects of the basic and the switching models around the infection-free state and the infected steady state from a local as well as a global perspective. Our aim is to study the role of harvesting and switching on the dynamics of disease propagation and/or eradication. A comparison of the local and global dynamical behavior in terms of important system parameters is obtained. Numerical simulations are done to illustrate the analytical results.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
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