A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING*

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ‘pest-eradication’ periodic solution and permanence of the system depend on time delay, hence, the authors call it “profitless”. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system. *This research is supported by the National Natural Science Foundation of China under Grant No. 10471117, 10771179, and the Natural Science and Development Foundation of Shandong University of Science and Technology under Grant No. 05g016.