Study On A Filippov Plant Disease Model With Insect-borne Transmission

Insect-borne plant diseases,i.e.insect as a carrier of pathogens,transmit virus to plants,which causes plant diseases,such as tomato yellow curl leaf virus trans-mitted by aphids,lettuce chlorosis virus transmitted by whitefly,maize line virus transmitted by leafhoppers,etc.Insect-borne plant diseases,as one of the main dis-eases threatening crops,have brought many health,social and economic problems.Therefore,it is necessary to formulate reasonable and effective control strategies to control the occurrence and development of plant diseases and insect pests in order to prevent and reduce the impact of diseases.Based on the transmission mecha-nism of insect-borne plant diseases,this paper adopts economic threshold strategy,establishes the Filippov vector plant disease model,and systematically studies the stability of the system under different thresholds.Firstly,we propose and analyze a mathematical model of Filippov insect-borne plant diseases with a threshold strategy,using infected plants as control indicators:if the number of infected plants does not exceed the threshold ET,no control measures will be taken;once exceeded,infected plants will be felled according to a certain proportion.The disease-free equilibrium point can be obtained by applying the comparison principle and constructing an appropriate Dulac function.The global asymptotic stability of the endemic equilibrium point is discussed,the dynamic behavior of the sliding system and the global dynamic system are analyzed.The numerical results show that the system is stable at the endemic equilibrium point of the two subsystems or at the pseudo-equilibrium point of the sliding system according to different threshold levels.Secondly,on the basis of the above part,a mathematical model of Filippov insect-borne plant diseases with two different threshold strategies was established.The infected plants and vector insects were taken as control indicators:if the num-ber of infected plants did not exceed the threshold Ic,no control measures were taken;if the number of infected vectors does not exceed the threshold value of Yc,but the number of infected plants exceeds the threshold value of Ic,only the infected plants need to be felled properly;if the number of both vectors exceeds their respective thresholds,not only the infected plants should be felled properly,but also a certain amount of vector natural enemies should be put in to control the further spread of the disease.By constructing the appropriate Dulac function and Green's formula,the global asymptotic stability of the corresponding equi-librium points of subsystems and sliding system are obtained,and the dynamic behavior of the system is systematically analyzed.The results show that the sys-tem can be stabilized at the endemic equilibrium point of two subsystems or at the pseudo-equilibrium point or pseudo-attractor of the sliding system by adopting two different threshold strategies.