On the use of reducible-functional differential equations in biological models

Biological models often lead to systems of delay or functional differential equations and to questions concerning the stability of equilibrium solutions of such equations. The monographs by Cushing [5] and MacDonald [ 1 1 ] discuss a number of examples of such models which describe phenomena from population dynamics, ecology, and physiology. The above-cited work of MacDonald is mainly devoted to the analysis of models leading to functional differential equations which are reducible to systems of ordinary differential equations. For example, consider the system