Analytic models of disease spread with birth, death, and concurrency

This writeup is intended to be an early draft showing progress in analytical models of the spread of an infectious disease through a population with non-negligible partnership duration and demographic turnover. We assume that individuals in the population form long-lasting (but not permanent) partnerships with others. New individuals enter the population at a constant rate, while others leave. The disease spreads through these partnerships. Our goal is to modify methods of [9] in order to incorporate “birth” and “death”. This is possible in a wide range of cases. In this writeup, we show how this is done for some simple cases, and compare the results with corresponding simulations. The analytic model is able to correctly predict behavior in the large population limit, with a dramatic reduction in run time and in the memory requirements. Please note that this is still a draft. Comments made in this font are intended to point out things that I have temporarily skipped over and need to address in more detail.