You might be interested in this exposure notification app https://www.covidwatch.org/. It's a collaboration between Stanford University and the University of Waterloo and it's pretty good. It will soon be more widely available.
The question is not the Software. That can be easily written. The question is how you would like to map the available information, schematically and/or logically. And how you want to collect the data.
The rest is easy.
If the data is sufficient and the desired answer can be projected from the available data, an AI can be created that can answer the necessary question.
If no such thing exists, I might take a stab at creating one -- so I'd even love to hear if you know of some causal-graph-inference-toolkit-thing that isn't specifically for COVID but seems like a promising foundation to build atop!
But, if no such thing exists, that also seems like evidence that it... wouldn't be useful? Maybe because very few social graphs have the communication and methodicalness to compose a detailed list of all the interactions they take part in? Conceivably because it's a computationally intractable problem? (I dunno, I hear that large Bayes nets are extremely hard to compute with.)
I would probably copy the MicroCOVID spreadsheet, and then write some custom logic into the cells that track people's microcovid levels. Seems like it wouldn't be too hard, and at the level of customization you want, I expect you would have to do something equally complicated with almost any other tool.
[bounty: $100 for recommending a tool that I use for more than two weeks]
I would love (and happily pay for) a piece of software that I could tell (a) a bunch of recent interactions between people ("Alice, masked, spent 3 hours, indoors, distanced, with Bob, unmasked, on Nov 1"), and (b) a bunch of evidence about their health over time ("Dolores tested negative on Nov 3"), and make queries about how likely various people are to have COVID.
I'd want it to be capable of complicated inferences like "Alice met with Bob yesterday; Bob met with Charlie 4d ago; Charlie separately met with Dolores that same day. Dolores just tested negative; given that, Alice is now less likely to be incubating COVID."
Ideally, it would take into account things like contagiousness-over-time profiles, and incubation periods, and asymptomatic cases, and how all those things differ between people, and tests' false negative rates -- but I realize that's a lot to ask.
Some non-solutions: