Infectious disease surveillance data often suffers from underreporting, posing challenges for studying disease dynamics at the population level. Traditionally, statisticians have approached this issue with skepticism, viewing the simultaneous estimation of reporting probability alongside other model parameters as infeasible without strong informative priors. In this talk, I will introduce Poisson Network Autoregressions (PNAR), statistical analogues to discrete-time susceptible-infectious-recovered (SIR) models, which leverage mechanistic information of disease spread to estimate reporting probability without relying on strong informative priors. Despite the promise of PNAR models, inference in the presence of underreporting poses significant challenges. I will discuss these challenges and present novel, practical Bayesian inference methods tailored for such models. Additionally, I will outline future research directions and advancements expected in the next 5 years.