  In this paper, we extend the logarithmic Euler-Maruyama scheme for stochastic
delay differential equation in one dimension to the part where we propose a
scheme for a system of stochastic delay differential equations. We then show
that the scheme always maintains positivity subject to initial conditions. We
then show the convergence of the proposed Euler-Maruyama scheme. With this
scheme, all the approximate solutions are positive and the rate of convergence
of this scheme is 0.5.
