Time delays in epidemic models: modeling and numerical aspects

In this course, we present some aspects of time delays in mathematical models of infectious disease transmission. We concentrate on delays originating from constant sojourn times in the various states of a system. In particular, we focus on a model of vaccination for a disease that confers no immunity.

The model under consideration is an integro-differential system. We show that choosing specific sojourn times description functions yields reduced models that undergo so called backward bifurcations.

In the case of a delay integro-differential system, this backward bifurcation is numerically investigated. Some considerations on numerical simulation of delay differential systems conclude this course.