Analysis On The Stability Of Three Kinds Of Eco-epidemiological Model

Infectious disease has existed in human history, it is not less than the naturaldisasters. The struggle between human and infectious disease has been sustained. In apredator-prey system, communication will have the disease between predator and prey;in agricultural production will have the disease spread between crop pests and diseases.Using ordinary differential equations to establish the corresponding model of impulsivedifferential equations, the mathematical knowledge to model the theoretical resultsobtained will provide beneficial help for the actual life. This paper studies three class ofinfectious disease model:The first category is the prey predator system with disease in the predator, predatorand prey by assuming is density dependent, and predator, infectious disease infectedpredator can recover but with temporary immunity, infectious disease model isestablished for a class of predator prey system, local stability analysis of thedisease-free equilibrium and the endemic equilibrium by using Eigen value method andHurwitzcriterion, the sufficient conditions for global asymptotic stability of thedisease-free equilibrium andtheendemic equilibrium isobtained byconstructing theLyapunov Function,namelytheepidemicdisease and nothreshold.The second class is given to harm now of crop pests in crop production caused bythe negative effects of spraying pesticides, and brings to the environment and humanhealth, the pest control strategy based on a class of pest management model, pulsetrapping and pulse on the pest saturation infectious rate is established, by using theFloquet multiplier theory comparison theorem to prove the persistence, globalasymptotic stability andsystem ofpest eradication periodic solution.Third kinds of model is a pulse on the virus particle and impulsive releasingnatural enemy model, based on second kinds of models, more factors are considered,the pulse releasing natural enemy and constant release natural enemy combination,comprehensive application of Floquet multiple methods to eliminate pests, more closeto the actual situation, through theory, differential equations and the comparisontheorem the pest eradication of local asymptotic stability and the globally asymptoticstability of periodic solution conditions, the perturbation technique of hungry persistentsystem with small amplitude.