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 nondgenerate M-matrices. The stability of equilibria for mathematical models in immunology and epidemiology is investigated.

中文翻译：

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生命系统模型中线性时滞微分方程的稳定性

我们介绍了对可分解为两个子系统的线性延迟微分方程组的平凡解的稳定性的研究结果。每个子系统都包含一种特殊形式的矩阵。我们根据稳定矩阵和非退化M矩阵的性质，建立了平凡解的渐近稳定性和非稳定性条件。研究了免疫学和流行病学中数学模型平衡的稳定性。