Amid the global challenge of mosquito-borne disease transmission, sterile insect technology (SIT) has emerged as a promising biological control strategy. Based on the classical Beverton–Holt model and the assumption of complete cytoplasmic incompatibility (CI), we develop a discrete-time model with overlapping generations and a corresponding integro-difference equation (IDE) to investigate the population dynamics under different release strategies for infected male mosquitoes. For the discrete-time model, we apply stability and bifurcation theory to determine the existence and stability of equilibria and derive the release threshold $r^{\ast }$ above which the wild mosquito population is successfully suppressed. Analysis of the IDE model yields a lower release threshold $r^{\ast \ast }$ and a critical patch-size $L^{\ast }$. Comparison of the two models demonstrates that spatial diffusion reduces the required release threshold for achieving population suppression.