General renewal equations motivated by biology and epidemiology

https://doi.org/10.1016/j.jde.2023.01.012Get rights and content
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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.

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.

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