Over the course of the year my fellow students and I have spent our free time building mathematical models of the spread of disease, initially assuming that upon contracting the infection a person would immediately and forever be infectious, then adding periods of incubation and recovery before finally introducing the concept of location whereby the proximate are significantly more likely to interact than the distant and examining the consequences for a population distributed between several disparate villages.
Whilst it is most certainly the case that this was more reasonable than assuming entirely random encounters it failed to take into account the fact that folk should have a much greater proclivity to meet with their friends, family and colleagues than with their neighbours and it is upon this deficiency that we have concentrated our most recent efforts.
My fellow students and I have spent the past several months attempting to build a mathematical model of the spread of disease, our interest in the subject having been piqued whilst we were confined to our halls of residence during the epidemic that beset us upon the dawn of the year. Having commenced with the assumption that those who became infected would be infectious immediately and in perpetuity we refined our model by adding a non-infectious period of incubation and a finite period of illness, after which sufferers should recover with consequent immunity and absence of infectiousness.
A fundamental weakness in our model that we have lately sought to address is the presumption that individuals might initiate contact with other members of the population entirely by chance when it is far more likely that they should interact with those in their immediate vicinity. It is upon our first attempt at correcting this deficiency that I should now like to report.
When last we spoke, I told you of my fellow students' and my first attempt at employing Professor B------'s wondrous computational engine to investigate the statistical properties of the spread of disease; a subject that we had become most curious about whilst confined to our quarters during the epidemic earlier this year. You will no doubt recall that our model assumed that once someone became infected their infectiousness would persist indefinitely, which is quite contrary to the nature of the outbreak. We have since added incubation, recovery and immunity and it is upon these refinements that I shall now report.
During the recent epidemic, my fellow students and I had plenty of time upon our hands due to the closure of the taverns, theatres and gambling houses at which we would typically while away our evenings and the Dean's subsequent edict restricting us to halls. We naturally set to thinking upon the nature of the disease's transmission and, once the Dean relaxed our confinement, we returned to our college determined to employ Professor B------'s incredible mathematical machine to investigate the probabilistic nature of contagion.