Application Of Pest Model With Infectious Diseases

Integrated pest management(IPM), under the premise of protecting the environ-ment, is the implementation of pest control measures, so that pest populations below the allowable level of economic victimization. And then we can get the best economic, social and ecological benefits. In this paper, considering the premise of integrated pest management, two type pest models with infectious diseases have been analysised and researched in-depth.In the second section, the principles of Finite-time Stability(FTS) will be intro-duced to integrated pest management. First, we will establish a class impulsive dynam-ic system(IDS) which contains a Lotka-Volterra model and a pulse-skipping equation. Then, the model should be studied as follows:(1)The instability about the positive equilibrium of the Lotka-Volterra system with-out impulse will be analysis.(2)Pulses is applied on the Lotka-Volterra system. By using Matlab LMI Controller Toolbox, the maximum-time interval of Finite-time Stability will be solved, and then pulse strategy can be formulated.(3)The state feedback controller is introduced to above pulse control system and use it to extend the impulsive maximum-time intervals. Finally, the validity of IPM policy could be verify by numerical simulation.In the third chapter, we established a simultaneous model about pest diseases, which include crops (pests growing source), a single parasite (split into three parts) along with diseases that through parasites vector-borne, and construct the correspond-ing differential equations system. Subsequently, we calculated and discussed the ex-istence of multiple equilibria and their local asymptotic stability, then the principle of pest populations persistence will be used to study the model depth. The conditions for solutions closed to equilibrium will be discussed by using Lyapunov function. So far, the use of parasites feature integrated pest is theoretically feasible. We can adjust the size of the input rate to control pest populations overall, that is consistent with the goal of integrated pest management.