# Article

**Keywords:**

delay differential equations; ordinary differential equations; Runge-Kutta methods; Newton-Cotes quadrature

**Summary:**

It is well-known that the environments of most natural populations change with time and that such changes induce variation in the growth characteristics of population which is often modelled by delay differential equations, usually with
time-varying delay. The purpose of this article is to derive a numerical solution
of the delay differential system with continuously distributed delays based on
a composition of $p$-step methods ($p=1,2,3,4,5$) and quadrature formulas. Some numerical results are presented compared to the known ones.