I don't see why that would affect anything. Y and Z are just numbers at each step- multiply those numbers

You are given X(0), Y(0), Z(0), so you can calculuate

dX= (-A*X(0) + B*Y(0)*Z(0))dt, dY= (A*X(0) - B*Y(0)*Z(0) - DY(0))dt, dZ= DY(0)dt

X(dt)= X(0)+ dX, Y(dt)= Y(0)+ dY, Z(dt)= Z(0)+ dZ

Now, dX= (-A*X(dt) + B*Y(dt)*Z(dt))dt, dY= (A*X(dt) - B*Y(dt)*Z(dt) - DY(dt))dt, dZ= DY(dt)dt

and X(2dt)= X(dt)+ dX, Y(2dt)= Y(dt)+ dY, Z(2dt)= Z(dt)+ dZ

and continue like that.

Now, I have replace Y' on the right sides of the last two equations with Y, assuming that was a typo. If not, the Y' equation can be rewritten (1+D)Y'= AX- B*Y*Z so Y'= (AX- B*Y*Z)/(1+D) and the Z' equation gives

dZ= d(dY/dt) where dY is calcated first, then dZ.