Counting the steady states of a rational ordinary differential equation issued from biology using algebraic methods

In this work, we present a method designed to count the steady states of a rational ordinary differential equation in the biological context of the adipose tissue, where multistability may arise. The method relies on the fact that the regions of the parameter space where the number of steady states does not vary can be defined through finitely many polynomial inequalities with respect to the parameters of the model, hence, paving the way to the use of algebraic methods for identifying those regions.