Abstract
The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given.
Highlights
In the natural world, no species can survive alone
We propose a predator-prey system, where the predator population P is assumed to be present in the system and the prey population N = S + I migrates into the system
Before we introduce the model, we would like to present a brief sketch of the construction of the model
Summary
No species can survive alone. While species spread the disease, compete with the other species for space or food, or are predated by other species, predator-prey relationship can be important in regulating the number of preys and predators. A general predator-prey model with Hassell-Varley type functional response may take the following form: dx dt. There are a lot of excellent works on predator-prey models with Hassell-Varley type functional response; for example, see [19,20,21,22] and the references therein. Motivated by these factors, a new nonautonomous predator-prey model with Hassell-Varley type functional response and the saturation incidence rate is proposed to give a more appropriate result and better understanding of the role of migratory birds in pathophoresis.
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