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.
MSC
35L65
92D30
Keywords
IBVP for renewal equations
Well posedness of epidemiological models
Differential equations in epidemic modeling
Age and space structured SIR models
Data availability
No data was used for the research described in the article.