A criterion for stability of matrices (Q1270933)

The authors derive a necessary and sufficient condition for the stability of an \(n\times n\) matrix with real entries using a simple spectral property of compound matrices. This result offers an alternative to the well-known Routh-Hurwitz conditions. As an application and demonstration of the effectiveness of these criteria, the asymptotic stability of a unique endemic equilibrium of an epidemic model of SEIR type with varying total population is proved. It is also shown that the verification of the Routh-Hurwitz conditions for this problem presents substantial technical difficulties.