<p>To study the effects of seasonal variation and climate change on the population dynamics of Aedes aegypti, we construct a reaction–diffusion model for Aedes aegypti on an asymptotic periodically evolving domain. Using the spectral radius of the next-generation operator and the related eigenvalue problem, we present the survival threshold of the model and its properties. Additionally, we apply the method of upper and lower solutions to establish the existence and attractivity of periodic solutions under different survival threshold conditions. In the final part of the theoretical analysis, we lift the global dynamics of the limit system to the original asymptotically periodic system with the help of the theory of chain transitive sets. Numerical simulations further demonstrate that the asymptotically periodic change of the domain plays a key role in the spread of Aedes aegypti.</p>