So far, my local Market Basket is showing no signs of shortages, no long lines (at least, not longer than usual), and no runs on products such as tissues, TP, etc. Of course, I live where people stock up for the winter so many of us still have large supplies of tissues, paper towels, TP, canned goods and the like. Cold winters, you know...
I'll let you all know if things have changed later this week. I do believe I will stock my freezer with chicken and other freezable things. My freezer's pretty small so no hoarding here.