Abstract
Plants play a vital role in the everyday life of all organisms on earth. This paper proposes a Filippov vector-borne plant disease model incorporating roguing of infected plants and spaying pesticides to relieve the economical devastation for growers and damage to humans, natural enemies and the environment. No control strategy is taken if the number of infected plants is less than an infected plant threshold level I_{c}; further, infected plants are removed once the number of infected plants exceeds I_{c}; meanwhile, pesticides are spayed if the number of infected vectors exceeds the infected vector threshold level Y_{c}. The global dynamics for the proposed system is investigated. Model solutions ultimately stabilize at the positive equilibrium that lies in the region above I_{c}, or on I=I_{c}, or below I_{c}, depending on the threshold values I_{c} and Y_{c}. The findings indicate that proper combinations of the infected plant and vector threshold values based on the threshold policy can maintain the number of infected plants either at a previously given level or below a certain threshold level.
Highlights
Plant viruses belong to the most limiting factors to modern agriculture, especially in lesserdeveloped countries
In order to relieve the economical devastate for growers by continuously roguing diseased plants and the damage to the environment, human health and natural enemies by spraying insecticides, in this paper, we consider a vector-borne plant disease model with Filippov–type control, that is, roguing and spraying insecticides are implemented only when the infected plants and infected vectors are beyond some tolerant thresholds
In the following four sections (Sects. 3–6), we address the richness of the dynamics that system (1) with (2) can exhibit, including the existence and stability of all the possible equilibria, and the existence of the sliding mode and its dynamics on the switching surfaces Ω1 and Ω2 by varying the threshold values Yc and Ic
Summary
Plant viruses belong to the most limiting factors to modern agriculture, especially in lesserdeveloped countries. Roguing (identifying and removal of diseased plants) is a well-known means of virus disease control measures with wide applicability [1]. In order to relieve the economical devastate for growers by continuously roguing diseased plants and the damage to the environment, human health and natural enemies by spraying insecticides, in this paper, we consider a vector-borne plant disease model with Filippov–type control, that is, roguing and spraying insecticides are implemented only when the infected plants and infected vectors are beyond some tolerant thresholds. Infected insects can transmit the virus to susceptible plants upon contact.
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