Mathematical modelling is useful for understanding infectious disease epidemics, and for estimating the impact of interventions to control them. However, the appropriateness of different modelling approaches depends on the local context and availability of data. In this thesis I use two approaches, epidemiological and evolutionary modelling, to estimate the impact of interventions for controlling HIV and COVID-19. After developing a dynamic transmission model fitted to local demographic, HIV prevalence and antiretroviral therapy (ART) coverage data, I estimated the impact of a 2-year real-world demonstration study of pre-exposure prophylaxis (PrEP) and ART treatment-as-prevention (TasP) among female sex workers (FSW) in Cotonou, Benin. I further estimated the impact of long-term scale-up scenarios of PrEP and TasP among FSW in Cotonou. Next, based on data collected during the 2020 COVID-19 epidemic in Benin, I simulated scenarios of COVID-related disruptions to HIV services and sexual behaviour, using the same dynamic transmission model. I estimated the impact of these disruptions on HIV epidemiology in Cotonou. Many non-pharmaceutical interventions (NPIs), including travel restrictions and lockdowns, were implemented globally to control COVID-19. Using model-based phylodynamic methods fitted to twenty SARS-CoV-2 genomes, I estimated the impact of NPIs in Weifang, China, one of the first COVID-19 epidemics outside of Wuhan. Finally, I performed several non-parametric phylodynamic analyses on the COVID-19 epidemic in England, fitted to thousands of SARS-CoV-2 genomes. I evaluated the association of stringency of NPIs and mobility with viral transmission at different periods between spring 2020 and winter 2020-2021. I further investigated the relative growth rates between different viral lineages, including the B.1.1.7 (’alpha’) variant. The results from this thesis are useful principally to policymakers for designing effective local control measures for HIV and COVID-19. While modelling can be used to estimate the impact of interventions, model choice must be tailored to the local epidemiological context.