What is a good model for assessing the effect of testing and contact tracing on R0?

I'm imagining it would have parameters perhaps like:

• testing frequency
• testing result delay
• time
• viral load (varies with time)
• testing false negatives (probably varies with viral load)
• path through environment (varies with viral load - i.e. if very sick they self isolate)
• number of people who intersect that path (perhaps weighted by distance and duration)
• emission filtration (aka masks)
• reception filtration (aka masks)
• percentage of the population tested on a regular frequency (or more complex arrangements if you wish to build that in)
• percentage of people who go into isolation if they test positive or are requested to do so as a precautionary measure because of the contact tracing conclusions
• contact tracing density - maybe only 50% of the population is part of the network
• how deep in the contact tracing web it is recommended to self isolate (perhaps varying with testing frequency because it spreads in time)
• the growth rate in time (which depends on a lot of the parameters above)
• some sums or integrals over time and when the testing occurred
• something something default parameters (some of which can be determined by the original R0 and doubling time of covid-19)
• something something initial conditions
• maybe including the percentage of the population already infected or recovered
• maybe something something pooled tests or randomized population testing
• maybe something something contact graph structure
• if very ambitious adding things like packages or perhaps other animals that may be able to catch and transmit it

Ideally it would be able to answer questions like: How much does it decrease R0 if you test 90% of people every 10 days with a false negative rate of 15%, an isolation compliance rate of 85%, a contact tracing web that is 50% dense, and a proactive quarantine over the contact tracing web that is two contacts deep?