The main object of study in this paper is an epidemic process on a large network in the presence of various public health interventions. As an example, we consider a simple Susceptible-Infected (SI)-type epidemic process on a Configuration Model (CM) random graph with public health interventions in the form of active random surveillance and contact-tracing. While infected individuals attempt to infect their neighbours, they themselves are at risk of removal due to random surveillance and contact-tracing. We allow the random graph to be constructed dynamically as an outcome of the spread of infection and removal due to contact-tracing. We study the large graph limit of these two competing processes (infection and contact-tracing) as the number of vertices grows to infinity. From the public health perspective, the large graph limit can be utilized to determine the optimal rates for surveillance and contact-tracing given a fixed budget constraint by formulating a suitable optimal control problem. Joint work with Soheil Eshghi, Eben Kenah, Forrest W. Crawford and Grzegorz A. Rempała.