The global dynamics and optimal control of a plant epidemic model

Hong Zhang, Mingming Su, Paul Georgescu

Abstract


This paper proposes and investigates a model for the spread of an infection into a plant population, considering the effects of both primary and secondary infections. We determine the basic reproduction number of the plant pathogens R0 and prove that if R0 > 1, then the positive equilibrium is globally stable, provided that several auxiliary inequalities, determined using the geometric approach of Li and Muldowney [23], hold. Also, we find a necessary condition for the existence of optimal controls by applying Pontryagin’s Minimum Principle. Finally, a numerical example is given to illustrate the applicability of our analytical findings.

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Published: 2015-10-10

How to Cite this Article:

Hong Zhang, Mingming Su, Paul Georgescu, The global dynamics and optimal control of a plant epidemic model, Communications in Mathematical Biology and Neuroscience, Vol 2015 (2015), Article ID 32

Copyright © 2015 Hong Zhang, Mingming Su, Paul Georgescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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