Diseases spread by the Aedes genus of mosquitoes are some of the fastest growing and fastest spreading viral pathogens in the world. Large dengue virus (DENV) epidemics have emerged in Fiji since the Second World War and there was widespread transmission of Zika virus (ZIKV) throughout the Pacific between 2013 and 2017. However, very few ZIKV cases were confirmed in Fiji. I conducted a serological survey in Fiji in 2017 and used these serological data, combined with mathematical modelling, to analyse transmission dynamics of arboviruses in Fiji. I found evidence for ZIKV circulation in Fiji between 2013 and 2015 followed by low ZIKV seroprevalence in 2017. I used paired serum samples to analyse the immunological response to ZIKV following outbreaks in Fiji and French Polynesia and found that neutralising antibodies declined in adults within two years of the outbreak in each country. I combined serological data with surveillance and molecular data to model unobserved ZIKV transmission and compare ZIKV and DENV transmission dynamics in Fiji. I found that the introduction time of a virus in Fiji could explain different transmission dynamics and concluded that ZIKV was likely introduced to Fiji in late 2014. I found high seroprevalence for all four DENV serotypes. I used a mathematical model of DENV transmission to analyse a DENV outbreak in 2017 to predict the duration and peak of the outbreak in real-time. I found that jointly fitting the model to a historic outbreak as well as the emerging outbreak improved the accuracy of the predictions from the model. Mathematical Modelling of Arbovirus Outbreak Dynamics in Fiji and the Wider Pacific Overall, I combined multiple data sources with mathematical modelling to reveal a diverse range of outbreak dynamics and serological responses to outbreaks of closely related viruses in the same location. I found that ZIKV and DENV do not necessarily generate a similar immune response in the same population and that both can cause low level multi-year outbreaks as well as large single season epidemics. Despite these challenges, mathematical modelling can improve our understanding of arbovirus outbreak dynamics such that it is possible to accurately forecast outbreak dynamics in real-time.