Based on my previous post, I have been stuck on this for a few hours now. I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$
The original two equations are: $$\frac{dx}{dt}=a-bx-\frac{cxy}{x+y} \\ \frac{dy}{dt}=\frac{cxy}{x+y}-(b+c+d)y $$
$a,b,c,d,x,y$ are all nonnegative.
What is the best strategy?