In contrast to ordinary differential equations (ODEs), delay differential equations (DDEs) allow for the inclusion of past actions into mathematical models, thus making the model closer to the real-world phenomenon. In population dynamics and epidemiology, delays are often used to represent transition through a certain stage of the life cycle (maturation delay) or of the disease (incubation time, immune period). The introduction of a single time lag into a classical ODE, turns the problem into an infinite dimensional dynamical system which often exhibits a richer behavior than its "ODE- equivalent".
In this talk I will present results emerging from the application of DDEs to model phenomena in population dynamics and epidemiology. I will particularly focus on questions related to existence, uniqueness and nonnegativity of solutions, as well as to stability of equilibria and the existence of bifurcations, especially in the case of state-dependent or multiple delays.