Abstract: Based on ecological security, sterile technology has gradually become the development direction of rodent control, which can control rodent population more permanently and thoroughly than poison. Combined with the valid period of sterilant, a single-species population under sterility control is established. After the discussion of the conditions for the existence of equilibrium points, the necessary and sufficient conditions are obtained for guaranteeing global asymptotic stability of the zero equilibrium points, and the sufficient condition is obtained for guaranteeing global asymptotic stability of the positive equilibrium point. In the end, the effects of contraception control and the valid period of sterilant on the dynamics of the pest population are analyzed.

Key words: contraception control, equilibria, global asymptotic stability