  The importance of the Hurwitz Metzler matrices and the Hurwitz symmetric
matrices can be appreciated in different applications: communication networks,
biology and economics are some of them. In this paper, we use an approach of
differential topology for studying such matrices. Our results are as follows:
the space of the $n\times n$ Hurwitz symmetric matrices has a product manifold
structure given by the space of the $(n-1) \times (n-1)$ Hurwitz symmetric
matrices and the euclidean space. Additionally we study the space of Hurwitz
Metzler matrices and these ideas let us do an analysis of robustness of Hurwitz
Metzler matrices. In particular, we study the Insulin Model as application.
