Branch of data science that covers event based time series?
"rather than aggregated values at evenly distributed intervals?" I think that part defines your question very well; i.e that is usually what we generally do in usual time-series problems, merging the events in some discrete time intervals. 

What you can do is that, you can give the time distance between the events as features, without giving evenly distributed intervals. For example, the exact time distances between events of every disease outbreak or every patient getting sick and etc. Moreover, you can do some feature engineering; squared time differences or percentage changes of time difference between the differences between the sequential doubles (x, x-1) and (x-1, x-2) where x-n,.....,x-2, x-1, x are the sequential events, not the time. 

The relevant concept here seems to be "unevenly spaced time-series", the wiki page Wikipedia: Unevenly spaced time series and this researcher's website http://eckner.com/research.html  seems to give enough material to get started with.