  Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed. Mathematical modeling of
biological systems with delays is usually based on Delay Differential Equations
(DDEs), a kind of differential equations in which the derivative of the unknown
function at a certain time is given in terms of the values of the function at
previous times. In the literature, delay stochastic simulation algorithms have
been proposed. These algorithms follow a "delay as duration" approach, namely
they are based on an interpretation of a delay as the elapsing time between the
start and the termination of a chemical reaction. This interpretation is not
suitable for some classes of biological systems in which species involved in a
delayed interaction can be involved at the same time in other interactions. We
show on a DDE model of tumor growth that the delay as duration approach for
stochastic simulation is not precise, and we propose a simulation algorithm
based on a ``purely delayed'' interpretation of delays which provides better
results on the considered model.
