Studying the behavior of solutions to the Cauchy problem for a family of nonlinear functional differential equations with delay which arise in the living system models, we establish the conditions that provide some exponential decay estimates for components of solutions. We find the parameters of simultaneous exponential estimates as solutions to nonlinear inequalities built from the majorants of the mappings on the right-hand sides of the differential equations. We present the results of constructing the exponential estimates for the variables in an epidemic dynamics model.

中文翻译：

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生命系统模型非线性延迟微分方程解的某些分量的指数衰减估计

研究在生命系统模型中出现的具有延迟的非线性函数微分方程族的柯西问题的解的行为，我们建立了为解的分量提供一些指数衰减估计的条件。我们发现同时指数估计的参数作为非线性不等式的解，这些非线性不等式由微分方程右侧的映射的主要项构建。我们展示了在流行病动力学模型中构建变量指数估计的结果。