Construction of exponentially decreasing estimates of solutions to a Cauchy problem for some nonlinear systems of delay differential equations

Abstract

The behavior of solutions for several models of living systems, presented as the Cauchy problem for nonlinear systems of delay differential equations is investigated. A set of conditions providing exponentially decreasing estimates of the components of the solutions of the studied Cauchy problem is established. The parameters of exponential estimates are found as a solution of a nonlinear system of inequalities, based on the right part of the system of differential equations. The results of studying mathematical models arising in epidemiology, immunology and physiology are presented.