Stability of linear delay differential equations arising in models of living systems

We present the results of our study of the stability of the trivial solution to a system of linear delay differential equations decomposable into two subsystems. Each of the subsystems contains matrices of a special form. We establish conditions for the asymptotic stability and nonstability of the trivial solution on the basis of the properties of stable matrices and nondegenerate $M$-matrices. The stability of equilibria for mathematical models in immunology and epidemiology is investigated.