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Chikungunya and dengue are re-emerging mosquito-borne infectious diseases that are of increasing concern as human travel and expanding mosquito ranges increase the risk of spread. We seek to understand the differences in transient and endemic behavior of chikungunya and dengue; risk of emergence for different virus-vector assemblages; and the role that virus evolution plays in disease dynamics and risk. To address these questions, we adapt a mathematical mosquito-borne disease model to chikungunya and dengue in Aedes aegypti and Aedes albopictus mosquitoes. We derive analytical threshold conditions and important dimensionless parameters for virus transmission; perform sensitivity analysis on quantities of interest such as the basic reproduction number, endemic equilibrium, and first epidemic peak; and compute distributions for the quantities of interest across parameter ranges. We found that …