The basic reproduction number is an important concept used in population biology and epidemiology. We will review its definition, and prove some of its properties that should clarify why it is such an ubiquitous notion in these fields. To motivate this talk, we shall apply these results in the context of Leslie's population model.
This may be the first in a series of lectures with the goal of extending the concept of the basic reproduction number to more general settings of linear operators on Banach spaces that leave a cone invariant. Since the major tool used in most of the proofs is the Perron-Frobenius Theorem, it is likely that we will spend some time to discuss certain parts of the proof of this celebrated result.