We would like to be able to use the positive/negative tests information in a useful way. Here is one possibility:
That is, each compartment (except ICU/hospital/dead) has a parallel ‘awaiting testing’ compartment. From there, individuals can move back into their original compartment (on the receipt of a negative test), or directly to the recovered compartment (if we assume that all individuals receiving a positive test will self-isolate), or into the next compartment in the epidemiological flow (e.g., if they progress from Exposed to Pre-symptomatic while awaiting test results). All individuals are testing on transition to H, if not before.
This should take care of test lags in a sensible way, although there are a bunch of questions/issues to resolve:
Integrate with material at private GitHub repo: