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Epidemics in predator-prey models: disease in the predators. (English) Zbl 1014.92036

Summary: The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one [Rocky Mt. J. Math. 24, No. 1, 381-402 (1994; Zbl 0799.92017)]. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model.

Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e., logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.

34C60Qualitative investigation and simulation of models (ODE)
34D99Stability theory of ODE