Re: Never fear, Jimmy Wales is here
Actually, his team probably can. I suspect anyone who has ever created an iOS/Android app could do it in a couple of weeks.
The only hard bit is defining when a given instance should broadcast its contacts list, as it'd be rather open to abuse to let users hit the panic button without any confirmation of a diagnosis.
Though on the other hand, it's not actually any worse than than asking people with a positive test to fill out an online form listing their contacts. And that is the current UK methodology.
So maybe a simple Big Red Button actually is ok.