Abstract
We study simple mathematical models for the dynamics of interactive wild and sterile insect populations. As well as being mathematically tractable, these models can be used as first approximations to real situations occurring with the Sterile Insect Technique (SIT) in which sterile males are released to reduce or eradicate a pest population. This is a method of biological control which can effectively help contain the spread of many pest insects such as the Red Palm Weevil (RPW). Models formulated in this paper are continuous-time, include a strong Allee effect that captures extinction events, and incorporate different strategies of releasing sterile insects. We perform basic studies of dynamical features of these models, with an emphasis on the condition of excitation, and the impact of the different release methods is investigated. Our findings are also demonstrated with some numerical examples.