In this study, two discrete mosquito population-control models incorporating the Allee effect are developed to investigate the impact of different sterile mosquito release strategies. By applying the theory of difference equations, a comprehensive analysis is conducted on the existence and stability of fixed points in scenarios with and without sterile mosquito releases. Conditions for the existence and stability of positive fixed points are rigorously derived. The findings reveal that in the absence of a positive fixed point, the wild mosquito population inevitably declines to extinction. When a single positive fixed point exists, the population dynamics exhibit dependence on the initial population size, potentially leading to either extinction or stabilization. In cases where two positive fixed points are present, a bistable dynamic emerges, indicating the coexistence of two mosquito populations.

Air pollution is one of the most important environmental problems in the world, it does harm to human health as well as hindering the sustainable development of the economy. The grim situation deserves wide attention and active participation in improvement. Thus, in this paper, considering the pollution control and sustainable development of the economy, we develop and investigate the economic-environment model with unilateral and bilateral control. To begin with, we briefly describe the dynamic behavior of the free system. It then follows the analysis of the system with unilateral and bilateral control. The existence of the order-1 and order-2 periodic solutions are investigated under different conditions. In addition, their stability is proven. The results show that the bilateral control strategy is beneficial to the sustainable development of economy.