Though instances of arthropod-borne (arbo)virus co-infection have been documented clinically, the overall incidence of arbovirus co-infection and its drivers are not well understood. Now that dengue, Zika and chikungunya viruses are all in circulation across tropical and subtropical regions of the Americas, it is important to understand the environmental and biological conditions that make co-infections more likely to occur. To understand this, we developed a mathematical model of co-circulation of two arboviruses, with transmission parameters approximating dengue, Zika and/or chikungunya viruses, and co-infection possible in both humans and mosquitoes. We examined the influence of seasonal timing of arbovirus co-circulation on the extent of co-infection. By undertaking a sensitivity analysis of this model, we examined how biological factors interact with seasonality to determine arbovirus co-infection transmission and prevalence. We found that temporal synchrony of the co-infecting viruses and average temperature were the most influential drivers of co-infection incidence. Our model highlights the synergistic effect of co-transmission from mosquitoes, which leads to more than double the number of co-infections than would be expected in a scenario without co-transmission. Our results suggest that appreciable numbers of co-infections are unlikely to occur except in tropical climates when the viruses co-occur in time and space.