Aedes aegypti female mosquitoes are the principal transmitters of dengue and other vector-borne infections. This species is closely associated with human habitation, due to its blood-feeding habits and the presence of breeding sites widely available around households. In this paper, we introduce a mathematical model for the life cycle of Aedes aegypti mosquitoes comprising two stages, aerial and aquatic, that reflects seasonal changes in the mosquito abundance. This model is further amended by three season-dependent control actions. Two coercive actions are introduced during the hot seasons characterized by higher abundance and enhanced growth rates of mosquitoes. They consist in the application of two chemical substances, insecticide and larvicide, acting upon the aerial and aquatic mosquito stages, respectively. During the cool seasons, characterized by the slower growth rates of mosquitoes and abundance of quiescent unhatched eggs, we introduce a preventive vector control measure consisting in mechanical elimination of mosquito breeding sites. Using the framework of optimal control in combination with the cost-benefit approach and epidemiological assessment, we identify the most efficient strategy capable of essentially reducing the population of adult and immature mosquitoes during both seasons and provide a sketch for its modus operandi.