Which tense to describe the analysis on a dataset?
In a case such as this, you need to use a careful mixture of tenses, because sometimes you are speaking about an event which is in the past, and sometimes you are speaking about an observation about that event, which still holds in the present.

Thus, in your example:


  We analyze the epidemic spreading dataset in 2008. Let I(t) represent the number of individuals that were infected at t. Our analysis shows that the epidemic had infected 100 individuals, and most of them were in the EU. The results show that on average each individual has three neighbors.


Notice that the facts about the events that occurred in 2008 are in the past tense, but the analytical results are in the present because the analysis is still showing these facts right now as the reader looks at it (I am assuming the "on average" result in your sample is a general conclusion and not just a fact about those 100 individuals in 2008).