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A criterion for stability of matrices. (English) Zbl 0911.15007
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.

MSC:
15A42Inequalities involving eigenvalues and eigenvectors
92D30Epidemiology
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References:
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