On monotonicity of solutions of nonnegative and compartmental dynamical systems with time delays

Nonnnegative and compartmental dynamical systems with time delay play a major role in describing many processes in biological and medical sciences. In the specific field of pharmacokinetics, the state variables of compartmental dynamical systems represent masses or concentrations of drug disposition from the body. Since drug concentrations should monotonically decline after discontinuation of drug administration, it is of interest to determine necessary and sufficient conditions under which these systems possess monotonic solutions. In a recent paper, necessary and sufficient conditions were developed for identifying nonnegative and compartmental dynamical systems that only admit nonoscillatory and monotonic solutions. In this paper we derive analogous results for nonnegative and compartmental systems with time delays.