Sorry, no specific number here, but my reasoning would approximately go like this:
First, how long can I afford to be self-quarantined? Buying food is not the main problem for me (I can cook, rice is cheap, I have enough money to hypothetically buy enough rice for a year); the limiting factor is how much vacation can I get, and whether I want to burn it all now. Even assuming that coronavirus is the highest priority, I suspect there may be two major waves of infection: one now, and one during the autumn. (Quitting is not an option; then I would have to pay my health insurance and would run out of money much faster.)
Second, assume exponential growth, until almost everyone is sick. Now you can estimate the peak, and time your self-quarantine so that it is around that peak.
The problem is, the noise in estimation of the peak is probably greater than my vacation time, so I can't really do this in practice. Oops.
The second best option is partial self-quarantine, that is reducing exposure to the minimum level I can keep for a few months. Try to work remotely whenever possible, never eat outside your home, reduce social activities to minimum. When? Well, I already started this week -- on Monday I asked my boss to let me work from home, started cooking every day, took my child out of kindergarten, and cancelled a birthday party this weekend. Seemed a bit paranoid... and then on Friday we got the first confirmed coronavirus case in my country.
I suspect someone else can come up with a more formal equation but I would say look at the local estimate of R-0 and then perhaps consider the old 6 degrees of separation claim.
However, I think a slightly different, non-quantitative way is carefully associating and knowing something about how those you associate are acting in this context. As soon as you start feeling like your exposure may no longer be based on secondary or tertiary sources it would be time to self quarantine.
[Edit -- I think it might be worth defining your population as well. Might not need to be the entire urban area/city/county but closer to neighborhood or apartment complex.)
I'm looking for a specific number here, even an equation. At what # of reported coronavirus cases (or estimated actual cases) within a population should the members of that population start self-quarantine measures (e.g. isolating themselves, avoiding contact with elderly, wearing masks)? Please state your reasoning, cite your sources, and/or show your math.
I know that being excessive in viral response is a good thing, and we should err on the side of doing too much, but I'm trying to be optimal in accounting for the behavioral costs of such measures.
Utah has 1 reported case. (source) It has a population of 3.161 million. The transmission rate of coronavirus in the US is around X (I don't actually know if there's a good source for this). Given these numbers for Utah, what is the "trigger point"- the ratio of (COVID-19 cases / population) at which we should self-quarantine? For example, we should begin self-quarantining when the number of CV cases reaches 1% of the population or 316,100 cases.
Or more fine-grained, what are the specific series of trigger points at which specific measures (mask-wearing, self-isolation, eliminating public gatherings) should begin?