# Criterion of positivity for semilinear problems with applications in biology

## TL;DR

This paper introduces a new positivity and well-posedness criterion for infinite-dimensional semilinear problems, with applications demonstrated in biology fields like epidemiology, predator-prey dynamics, and oncology.

## Contribution

It provides a broad, weak-assumption-based criterion for positivity and well-posedness applicable to various semilinear problems, supported by biological examples.

## Key findings

- Criterion applies to diverse biological models
- Ensures positivity and well-posedness under weak assumptions
- Validated through epidemiology, predator-prey, and oncology cases

## Abstract

The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.