Arboviruses, or viruses spread by arthropods, affect billions of people each year. I focus on three arboviruses – dengue, chikungunya, and Zika viruses – all spread by the same Aedes spp. mosquitoes. In this dissertation, I present three mathematical analyses and one discussion aimed at understanding spatiotemporal variation in patterns of arboviral disease incidence.First, to quantify the extent of misdiagnosis among co-circulating dengue, chikungunya, and Zika during the 2015-2017 Zika epidemic in the Americas, I used basic principles of probability paired with empirical estimates of misdiagnosis rates. Across 43 countries, I generated revised estimates of Zika incidence data that accounted for the accuracy of diagnoses made on the basis of clinical presentation with or without molecular confirmation. I estimated that the Zika epidemic was likely 39.0% (95% CrI: 30.2%-46.7%) larger than the 679,400 cases reported in passive surveillance data.Second, to disentangle drivers of seasonal dengue epidemics in Guangzhou, China, I fitted a model to time series data from 2005-2015 and performed simulation experiments with the fitted model. I evaluated imported dengue cases, mosquito density, temperature, and residual variation in other local conditions as potential drivers of dengue incidence. My results indicated that while epidemics in most years were limited by unfavorable conditions with respect to one or more factors, an anomalously large epidemic in 2014 was made possible by the combination of favorable conditions for all factors considered in our analysis.Third, to test the effect of alternative model assumptions on forecasts of incidence and spread of emerging infectious diseases, I designed an ensemble of forecasting models in the context of the 2015-2016 Zika epidemic in Colombia. In the ensemble of models, I considered multiple alternative forms across three assumptions: spatial variation in the reproductive number, the role of human connectivity in transmission, and the number of introduction events. I assessed forecast performance through time and found that at different points in the epidemic, different forms of these assumptions performed best. Fourth, to consider the interplay between human behavioral changes and risk of arbovirus infection, I assessed the potential impact that an augmented reality game could have on people spending time outside, inadvertently elevating their risk of exposure to arboviruses. Using data from Twitter, I found that the time of day that individuals were most engaged in outdoor augmented reality games coincided with times of the day that disease-relevant mosquitoes were most likely to engage in blood-feeding. In conclusion, my research demonstrates that both specific knowledge of spatiotemporal variation in emerging arboviruses and general knowledge about phenomena affecting emerging infectious diseases are necessary for mitigating uncertainty in forecasts of emerging infectious diseases.