General Renewal Equations Motivated by Biology and Epidemiology

TL;DR

This paper introduces a unified mathematical framework for renewal equations, ensuring well-posedness and stability, applicable to diverse biological and epidemiological models including pandemic spread scenarios.

Contribution

It provides a general, versatile approach to analyze renewal equations with complex interactions, extending applicability to nonlinear, nonlocal, and boundary-involved models.

Findings

Framework guarantees well-posedness and stability.

Applicable to Covid-like epidemic models.

Includes models with low regularity and nonlocal interactions.

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.