Sufficient conditions for stability of linear differential equations with distributed delay

We develop conditions for the stability of the constant (steady state) solutions of linear delay differential equations with distributed delay when only information about the moments of the density of delays is available. We use Laplace transforms to investigate the properties of different distributions of delay. We give a method to parametrically determine the boundary of the region of stability, and sufficient conditions for stability based on the expectation of the distribution of the delay. We also obtain a result based on the skewness of the distribution. These results are illustrated on a recent model of peripheral neutrophil regulatory system which include a distribution of delays. The goal of this paper is to give a simple criterion for the stability when little is known about the distribution of the delay.