Given some (but not all) monthly totals of people with measles (or counts of product-units sold, or counts of retweets), how can we recover the weekly counts? This is an under-determined problem where assumptions on the data are necessary. Requiring smoothness between successive weeks is reasonable, but can we do better, if we have some domain knowledge? In our proposed method, GB-R, we incorporate our domain knowledge into our algorithm by introducing a specific epidemics model called SIS model. In this work, we show how to inject the domain knowledge into our algorithm, creating a gray-box model for reconstructing finer scale (weekly patient counts) epidemiological data given data in larger granularity (monthly counts). Experimental results on the Tycho dataset show that GB-R is effective, in reconstructing real-world epidemiology data, and interpretable in estimating the parameters of the gray-box model that align well with the epidemiological knowledge.