  In this paper, we investigate the dynamical behavior of a two-dimensional
discrete mosquito model incorporating an Allee effect. We analyze the system's
trajectory comprehensively, examining both local and global dynamics. Our
analysis begins by establishing the invariance of the positive trajectory
within the first quadrant. We then investigate the existence of fixed points
within this region. Following this, we perform a stability analysis to
determine both local and global asymptotic stability of the identified fixed
points. Finally, we validate the effectiveness and applicability of our
theoretical results through numerical examples.
