Exponential decay estimates for some components of solutions to the nonlinear delay differential equations of the living system models

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.