Someone just asked the mailing list (not realizing that the thread is on the message board instead) the following question: "How about 1793-1795 - 2 parents mid-30's and at least 1 child in the same family."

I suspect that there were several epidemics over the early years. I became interested several weeks ago in seeing what patterns might emerge, so I have been assembling a list of deaths in Guilford's first 70 years. I am not finished with the list or with consulting sources, but I am seeing other time periods (like the mid-1830's) when deaths within family groups seem higher than what I'd expect. I am putting the data on several pages that are linked under "Death" on the Vital Records page of Guilford County NCGenWeb.
http://www.ncgenweb.us/guilford/

As to what could cause these peaks, I don't know. I would be inclined to blame it on contagious illnesses and/or environmental factors.

Here is one website with lists of epidemics. You will see the US ones listed near the bottom:

http://en.wikipedia.org/wiki/List_of_epidemics

I have wondered whether part of the deaths in 1816 were a result of the "Year Without A Summer," due to a volcanic explosion in Southeast Asia.

http://en.wikipedia.org/wiki/Year_Without_a_Summer

Spring is also a prime time of year for pneumonia secondary to a winter influenza infection. There were a lot of pneumonia cases the spring after the Hong Kong flu epidemic in the winter of 1968-69. Without modern antibiotics, and with environmental changes going on, the population would be vulnerable to increased mortality.