This. I have told countless people "stay calm, do not panic." Don't fall victim to mass hysteria just because demasses are dumbasses.
As is often said, people are poor judges things like their risk to various adverse events and what's truly important in a crisis. People are scared of dying in a terrorist event; they don't think about their risk of dying in a car accident, which is FAR more likely to happen to them. They're scared about COVID-19 and are taking fanatical precautions, but don't bat an eye at preventing the flu. [Note: don't @ me about risk of dying or anything like that; I'm taking about general behavior toward prevention.] I can go on and on here.
With respect to going to the stores, they completely overestimate what they need to get through say 2 weeks. Most likely, they have enough food and cleaning supplies and so on to get through 2 weeks already. (Hell, they probably have enough hand sanitizer and cleaning supplies to get through a year because they rarely ever use them in the first place.) You may not like what you're eating some days, but you can eat it and easily survive. People are stocking up and in most cases probably now have enough food to comfortably go 8-10 weeks without needing to stretch. Add the ability to make food from scratch (increasingly a lost skill), and you can go even longer in both scenarios.
And maybe we need that kind of illustration. What do you really need at home to make it say 3 weeks without going out? Put out that list everywhere so people see it, and have them compare that list to what they have on hand. Most likely, they need very little beyond what they have.