短效不育剂控制下季节性繁殖害鼠种群的动态模型

害鼠给人类带来很大的危害，人们可以利用杀鼠剂和不育剂对其进行控制.害鼠在摄食不育剂后导致不育，但有时不育鼠会恢复生育能力，生育后代，使种群规模增大.本文建立了灭杀控制和短效不育控制下害鼠种群的动态模型，在模型中每隔固定时间施行两种控制，在害鼠的繁殖具有季节性的前提下，分析了模型的形态以及害鼠不育率、灭杀率、控制间隔、不育剂有效期等参数对种群动态的影响.结果表明： 较高的不育率和灭杀率，以及较短的控制间隔会达到更好的控制效果，可以使种群较小，甚至灭绝.短效不育剂限制了不育剂在控制害鼠上的作用，也降低了控制的效果.在使用短效不育剂控制害鼠的情况下，在繁殖季节后期，害鼠种群会有小的恢复.

Dynamic model of seasonal breeding rodent pest population controlled with short-acting sterilant

Rodent pests bring great damage to human beings, while rodenticide and sterilant can be used to control the pests. After ingesting sterilant, rodent pests lose their fertility, but in some cases, the sterile individuals may gain their fertility again, produce offspring, and enlarge population size. In this paper, the dynamic models of rodent pest population under lethal control and short-acting contraception control were formulated, and, with the prerequisite of the seasonal breeding of rodent pest population, the models were used to regularly analyze their behaviors and the effects of the contraception rate, lethal rate, control interval, and sterilant valid period on the dynamics of the pest population. The results showed that larger contraception rate and lethal rate and shorter control interval could have better control effect, making the controlled population become smaller and even died out. Short-acting sterilant limited the control effect. At the later period of breeding season, the rodent pest population controlled with short acting sterilant would have a weak recovery.