The Aedes aegypti mosquito inhabits most tropical and subtropical regions of the globe, where it transmits arboviral diseases of substantial public health relevance, such as dengue fever. In subtropical regions, Ae. aegypti often presents an annual abundance cycle driven by weather conditions. Because different population states may show varying responses to control, we are interested in studying what time of the year is most appropriate for control. To do so, we developed two dynamic site-occupancy models based on more than 200 weeks of mosquito trapping data from nearly 900 sites in a subtropical Brazilian city. Our phenomenological, Markovian models, fitted to data in a Bayesian framework, accounted for failure to detect mosquitoes in two alternative ways and for temporal variation in dynamic rates of local extinction and colonization of new sites. Infestation varied from nearly full cover of the city area in late summer, to between 10% and 67% of sites occupied in winter depending on the model. Sensitivity analysis reveals that changes in dynamic rates should have the greatest impact on site occupancy during autumn and early winter months, when the mosquito population is declining. We discuss the implications of this finding to the timing of mosquito control.