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Respiratory viruses cause substantial health and economic burdens. These viruses circulate concurrently, and changes in host susceptibility brought about by infection by one virus has the potential to change the transmission dynamics of another. Understanding the effects of such cross-protection between viruses at a population level can inform public health policies. Current evidence for cross-protection between these viruses mainly comes from population level shifts in dynamics, which cannot assess causation, and from small-scale biological experiments. I use mathematical modelling to research cross-protection between respiratory viruses, as these methods allow for testing of the mechanism. Initially, I develop a two-pathogen interaction model parameterised to simulate influenza and RSV epidemiology in the UK. Using a surveillance-like stochastic observation process I generate a range of possible trajectories, and then back-infer the parameters using Markov Chain Monte Carlo. I found that the strength and duration of influenza and RSV interaction could be estimated well; however, the robustness of inference does decline towards the extremes of the plausible parameter ranges, with misleading results. Next, I use parallel tempering to fit an adapted two-pathogen model to a unique dataset from Vietnam. I show that the population level-dynamics of influenza and RSV circulation support either moderate or no cross-protection. However, I add evidence that co-infection increases the rate of reporting. The benefits of limiting severe co-infection by vaccination in this setting may therefore outweigh the increased transmission that occurs due to cross-protection between the viruses. Finally, I use coronavirus surveillance data from England and Wales to estimate key seasonal coronavirus (HCoV) parameters, and I use these estimates to investigate age-specific susceptibility to SARS-CoV-2, varying the interaction assumption. I show that while cross-protection between HCoV and SARS-CoV-2 may contribute to the age distribution, it is insufficient to explain the observed reduced susceptibility of children. Collectively, the research in this thesis demonstrates that surveillance data and mathematical models can be used to study respiratory viral interactions. It implies that while models can be used to study this phenomenon, stochasticity can obscure results. The research also alleviates concerns that vaccination against influenza or RSV may have a detrimental impact on the other virus, due to interaction, although this must be investigated further to understand the generalisability of the results to other settings. Finally, the research implies that other factors must influence susceptibility to coronaviruses, and the observed shifting of epidemic peaks that has been hypothesised to be a result of respiratory viral interaction.