Stability of functional differential equations in mathematical epidemiology and ecology: when do delayed effects affect the outcome?

点击翻译按钮获取中文摘要

When a biological system oscillates, one of the usual suspects is delay. That is, we suspect that the underlying rules that govern how the system changes depend, to some degree, on the state of the system at an earlier time. For example, current human population growth is affected by the population size nine months ago. In some cases a delay does not have any significant effect, and so we say the delay is harmless. The main objective of my research program is to study the effect that delayed influences have on models in epidemiology, including determining when these delays are harmless. As more delays are introduced into a system, it may seem inevitable that oscillations would occur, however this is not always the case. It seems that there are certain strongly stabilizing qualities associated with epidemic models. Unfortunately, there is not a full understanding of what these qualities are. In summary, when are delays harmless and why?