The context of this work is the control of the Mediterranean fruit fly Ceratitis capitata in orchards in Corsica (France). It aims at optimizing the deployment of the Sterile Insect Technique (SIT) in an agricultural context. SIT is a biological control technique based on mass-rearing, radiation-based sterilization, and releases of the pest species targeted for population control. The sterilization process is subject to a trade-off: radiation doses should be high enough to effectively sterilize the males, but not too high to preserve their ability to attract females and mate. Among the releases a proportion of the irradiated pupae may therefore lead to non-sterile males. To represent the pest dynamics when sterile males are released, we have built a mathematical model based on differential equations, consisting of three compartments: sterile males, wild males and wild females. With this model, we compared three cases: perfect male sterilisation, contrasted with two situations in which residual fertility is taken into account, associated either with or without a fitness cost. We varied the residual fertility level and the associated fitness cost and studied their influence on the population dynamics by means of analytical studies (equilibria, stability, bifurcations) illustrated with simulations of the model calibrated for C. capitata. We have shown that when residual fertility is below a threshold value, wild populations can be driven to extinction by flooding the landscape with sterile males, generalizing the results presented in [1]. As expected, too high a level of residual fertility makes SIT less effective and hinders population control. Finally, the presence of an associated fitness cost, which is very likely, has a significant impact on control efficiency and generates a higher level of acceptable residual fertility. In practice, with the model calibrated to the biological parameters of C. capitata and for a 1% residual fertility rate, value generally obtained, a min- imum of 300 sterile males per day per ha would be required to theoretically eradicate the pest population.