Title: Criterion of positivity for semilinear problems with applications in biology,
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.