Modeling plant virus propagation with Filippov control

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 30
• Main Authors: Yang, Youping, Zhang, Tiantian
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 04.09.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Difference and Functional Equations; Flowers & plants; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Pesticides; Plant disease; Plant diseases; Roguing; Sliding mode; Threshold policy; Vector-borne; Viruses; Threshold policy; Roguing; Sliding mode; Plant disease; Vector-borne
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02921-5

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.