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. (c) 2023 Elsevier Inc. All rights reserved.
General renewal equations motivated by biology and epidemiology
Colombo R. M.
;Garavello M.;Marcellini F.;Rossi E.
2023-01-01
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. (c) 2023 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
