Abstract
In this paper, a four-populations’ nonlinear mathematical model is introduced to analyze the interactions between two different microorganisms and the olive tree on which they reside. One such microorganism infects and ultimately kills the branches while the other one has a beneficial effect on the plant. We aim at devising a control strategy of the action of the pathogenic microorganism on the plant. To this end, the equilibrium points of the ecosystem are investigated. Feasibility and stability conditions of the equilibria are derived analytically. The numerical simulations show that the infection transmission rate and the disease-related mortality can deeply affect the spread of the disease. Some conditions for the disease eradication are investigated and suggestions are given for the implementation of suitable biological controls, such as pruning of the infected leaves.
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Acknowledgements
This research has been partially supported by The European COST Action: FA 1405—Food and Agriculture: Using three-way interactions between plants, microbes, and arthropods to enhance crop protection and production. The research of Ezio Venturino has been partially supported by the project “Metodi numerici nelle scienze applicate” of the Dipartimento di Matematica “Giuseppe Peano.”
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Berardo, C., Bulai, I.M., Venturino, E., Baptista, P., Gomes, T. (2018). Modeling the Endophytic Fungus Epicoccum nigrum Action to Fight the “Olive Knot” Disease Caused by Pseudomonas savastanoi pv. savastanoi (Psv) Bacteria in Olea europaea L. Trees. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_13
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