Mathematical Study On A Pest Management SI Model With Impulsive Control Of Different Frequency

With the development of society and economy and the progress of science and technology,the problem of pest management gradually becomes one of the common research topics by allthe countries around the world. The main methods of pest management are chemical controland biological control. Considering the effectiveness of the above two methods, a kind of pestmanagement SI model with impulse control of different frequencies are proposed and thedynamical properties of the given models are studied.In Chapter1, we give some relevant preliminaries.In Chapter2, considering the control strategies of spraying pesticide and releasing infectedpest and natural enemies with different frequencies, we establish a pest-natural enemy SImodel. We suppose that the pest population is divided into susceptible pests and infectedpests, and natural enemies only predate the susceptible pests. Under the two special cases, i.e.spraying either more or less frequently than the releases, the sufficient conditions of existenceand global attractiveness of extinction periodic solution of susceptible pest is obtained.Moreover, we investigate the effects of the pest control tactics on the threshold conditions.We also show that the system has rich dynamics including period-doubling bifurcations andchaos as the release period increases. Finally, to see how the pesticide applications could bereduced, we develop a model involving periodic releases of natural enemies with chemicalcontrol applied only when the densities of the susceptible pest reaches the given EconomicThreshold (ET). And we obtain that the hybrid method is the most effective method to controlpest and the frequency of pesticide largely depends on the initial densities, ET and releasingperiod.In Chapter3, considering the control strategies of spraying pesticide and releasing infectedpest with different frequencies, we establish a prey-pest SI model. We show that the sufficientconditions of existence and global attractiveness of extinction periodic solution of susceptiblepest for the given model under the two special cases, i.e. spraying either more or lessfrequently than the releases. In addition, we verify the correctness of the theoretical resultsand give the relevant factors which affect pest control strategies by numerical analysis.