Global Dynamics of a Discrete Mosquito Model with Allee Effect

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.