Question
TWO YEARS AGO I PLANTED A CURLY RED WILLOW APPROXIMATELY 6' FROM THE LAKE THAT I LIVE ON. IT GREW TO WHAT SEEMED LIKE 5 TO 7' AND WAS VERY HEALYHY. BUT THIS YEAR MEDIUM SIZE ANTS HAVE INVADED IT, AND IT NOW HAS MANY DEAD BRANCHES AND HAS LOST MOST OF ITS LEAVES. (I LIVE IN TUPELO MISSISSIPPI AND THE TREES ARE JUST NOW CHANGING AND HAVE NOT DROPPED) I SPRAYED ANT SPRAY (STORE BOUGHT) ON THE BASE OF THE TREE THINKING THIS MIGHT STOP THEM FROM CLIMBING, NO GO. IT WAS COVERED WITH THE ANTS EACH TIME I WOULD CHECK IT. I WOULD SO APPRECIATE ANY ADVISE TO SAVE THIS BEAUTIFUL WILLOW. THANK YOU, VAUGHN  

Answer
Sounds like a scale insect probably willow scale. These insects attach to the twigs and suck the plant juices from the tree. They secrete a sticky substance called honeydew, which is high is sugar content. The ant are feeding on the honeydew-control the scales and the honeydew will go sway and so will the ants.  You can control the scale insects with a soil applied insecticide called Bayer Advanced Tree and Shrub Insect Control. This is applied to the soil around the tree and watered in good. It takes a week or so for the roots to transport the insecticide to the twigs and when the scale sucks the plant juices they are killed. Here is a web link to this product. You should be able to get it at your local nursery. There are other insecticides that can be sprayed on the tree but these need to be sprayed for best results before the insect forms a scale (shell).  
http://www.bayeradvanced.com/product/Tree-Shrub-Insect-Control/concentrate.html