SIR Model and Information/ Innovation Economics
I'm not familiar with this area, so I can't tell you what are the seminal works, etc., but a quick search finds Gurley &amp; Johnson (2017) "Viral economics: an epidemiological model of knowledge diffusion in economics":


  We model the diffusion of economic knowledge using an epidemiological model of susceptible, exposed, infected/inspired, and recovered populations (SEIR). Treating peer-reviewed journal publications as evidence of a scholar’s infection/inspiration with energy for an idea or theme, we estimate the coefficients of a four-equation simultaneous system for each of 759 sub-fields of economics. Results show that some sub-fields of economics (or viruses, here) grow endogenously much faster than others, and just over half have basic reproduction properties sufficient to ensure survival without the annual addition of new protégé scholars.


Which in some sense is amusing because it's applying the model to economics knowledge/research itself. (The paper looks like it has been in draft out there for a while; there's one dating back to 2011, which is freely available on SSRN.)

I suspect the paper cites some other relevant work(s) in this area.