General renewal equations motivated by biology and epidemiology

Abstract

We present a unified framework ensuring well posedness and providing stability estimates to a class of Initial – Boundary Value Problems for renewal equations comprising a variety of biological or epidemiological models. This versatility is achieved considering fairly general – possibly non linear and/or non local – interaction terms, allowing both low regularity assumptions and independent variables with or without a boundary. In particular, these results also apply, for instance, to a model for the spreading of a Covid like pandemic or other epidemics. Further applications are shown to be covered by the present setting.