In this presentation, I will give an overview of several research problems that have been the focus of my recent work or are currently in active development. First, motivated by the recent COVID19 pandemic, I will discuss the concept of one-shot intervention, involving a singular intervention of limited duration. Moreover, I will present some illustrative models addressing the problem of optimal allocation of care-workers for domiciliary care services and investigating the impact of 'bubbling,' where single-parent households mutually nominate another household for support, both in the context of minimising disease burden. Shifting the focus, I will delve into the intricate task of deducing contact network properties from population-level epidemic data. I will explore two distinctive approaches. The first approach involves learning network structures a priori, subsequently integrating them as priors within a Bayesian framework. The second approach takes a more theoretical route, employing the pairwise model to infer network properties. Finally, I will present new findings concerning the spread of infection mediated by higher-order structure. To disentangle the impact of network structure from the dynamics on the network, I will formulate exact transmission models on fully connected networks involving an arbitrary number of simplexes ranging from transmission mediated by pairwise interactions up to and including k-simplices. By employing bifurcation analysis on the resulting exact mean-field models, I will illuminate a spectrum of emerging new phenomena characterised by multi-stability.