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Stability and bifurcation in plant-pathogens interactions. (English) Zbl 1410.92118

Summary: We consider a plant-pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory-inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology
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