# American Institute of Mathematical Sciences

2015, 12(3): 473-490. doi: 10.3934/mbe.2015.12.473

## The effect of time delay in plant--pathogen interactions with host demography

 1 Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples 2 Department of Mathematics, University of Portsmouth, Portsmouth, PO1 3HF, United Kingdom

Received  April 2014 Revised  November 2014 Published  January 2015

Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation.
Citation: Bruno Buonomo, Marianna Cerasuolo. The effect of time delay in plant--pathogen interactions with host demography. Mathematical Biosciences & Engineering, 2015, 12 (3) : 473-490. doi: 10.3934/mbe.2015.12.473
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