content_image/297573.jpg content_image/297574.jpg
Applying Routh-Hurwitz conditions [5] the unique equilibrium of the above system is locally asymptotically stable if the following conditions are satisfied: 

<img src='content_image/297573.jpg'>

For the special case r 1 = r 2 the above results simplifies significantly. The unique equilibrium solution become 

The existence and stability conditions are 

<img src='content_image/297574.jpg'>

