With a low Rt, will New York quarantine out-of-staters entering New York??

After New York Governor Cuomo's briefing on June 12, 2020, which included text



Rate of Transmission [Rt[ of .77 Lowest Out of All 50 States

(...)

So we are the exact opposite. We, since we've reopened, the number has continued to go down, believe it or not. We reopened. It continues to go down because we've been disciplined in our reopening, and that's what we have to continue to do. This is a website where the founders of Instagram now track the rate of transmission of states across the nation. New York State, the lowest rate of transmission, meaning the virus is spreading at the lowest rate in the State of New York, of every state in America, that is incredible. We were the number one state in terms of infection, number one in the nation, number one on the globe per capita, and now we're the last state in terms of rate of transmission. That is because New Yorkers stepped up, they were smart, they were disciplined, they did what they had to do, and we have to stay there. We have to stay there. Now is no time to forget what got us here. We have to stay smart.



***
link: https://www.governor.ny.gov/news/video-audio-rush-transcript-governor-cuomos-covid-19-update-new-york-has-nations-lowest-rate

***
I joked to a friend that the next thing that would happen would be an attempt by New York to quarantine out of state people coming INTO New York.

Well, one only had to wait till Monday, June 15. The CBS880 link paraphrases Cuomo's remark as


The governor says a primary concern right now is contagion coming from outsiders who are visiting New York.



link: https://wcbs880.radio.com/articles/news/cuomo-threatens-action-over-coronavirus-rule-violations

The actual audio is a bit more interesting.

****Separately, some background on Ro

From wikipedia:

During an epidemic, typically the number of diagnosed infections N(t) over time t is known. In the early stages of an epidemic, growth is exponential, with a logarithmic growth rate[citation needed]

{\displaystyle K={\frac {d\ln(N)}{dt}}.}
For exponential growth, N can be interpreted as the cumulative number of diagnoses (including individuals who have recovered) or the present number of diagnosed patients; the logarithmic growth rate is the same for either definition. In order to estimate R_{0}, assumptions are necessary about the time delay between infection and diagnosis and the time between infection and starting to be infectious.

In exponential growth, K is related to the doubling time T_{d} as

{\displaystyle K={\frac {\ln(2)}{T_{d}}}}.
Simple model[edit]
If an individual, after getting infected, infects exactly R_{0} new individuals only after exactly a time \tau (the serial interval) has passed, then the number of infectious individuals over time grows as

{\displaystyle n_{E}(t)=n_{E}(0)\,R_{0}^{t/\tau }}
or

{\displaystyle log(n_{E}(t))=log(n_{E}(0))+log(R_{0})t/\tau .}
In this case,

{\displaystyle R_{0}=e^{K\tau }} or {\displaystyle K={\frac {\ln R_{0}}{\tau }}}.
For example, with {\displaystyle \tau =5~\mathrm {d} } and {\displaystyle K=0.183~\mathrm {d} ^{-1}}, we would find {\displaystyle R_{0}=2.5}.


link: https://en.wikipedia.org/wiki/Basic_reproduction_number

Definitions from article by Y. Ma (2018) [
Epidemiol Infect. 2018 Sep; 146(12): 1478–1494.
Published online 2018 Jul 4. doi: 10.1017/S0950268818001760
]

The reproductive number and serial interval (SI) are two key quantities in describing transmission of an infectious disease. The reproductive number is defined as the average number of secondary cases a primary infectious case will produce. In a totally susceptible population, it is referred to as the basic reproductive number (R0); it is referred to as the effective reproductive number (Re) if the population includes both susceptible and non-susceptible persons [6]. An Re greater than 1 indicates that the disease will continue to spread while an Re less than 1 indicates that the disease will eventually die out. Although the reproductive number is usually defined as the average number of secondary cases, it is occasionally defined as the average number of secondary infections [7–10], a distinction that is important for a disease with a long incubation period (the time between infection and developing symptomatic disease) and/or only a fraction of infections progressing to disease. Depending on the setting, the reproductive number can be expressed as a function of parameters such as infection rate, contact rate, recovery rate, making it useful in determining whether or not a disease can spread through a population.

The serial interval (SI), defined as the time between disease symptom onset of a case and that of its infector [11], is a surrogate for the generation interval— an unobservable quantity defined as the time between the infection of a case and the time of infection of its infector [12]. The SI is an important quantity in the interpretation of infectious disease surveillance data, in the identification of outbreaks, and in the optimization of quarantine and contact tracing.

[lbe note: the serial interval is the time between when the infector shows symptoms and the infectee shows symptoms. If asymptomatic people can infect others, one immediately sees a problem here. R becomes undefined if tau becomes undefined.]

***As to covid19, one would have to estimate serial interval from information OUTSIDE OF new cases/per day, but this could be done and such number would be expected to be a known number with a range of uncertainty.
However, R is not knowable from new cases per day or from any data available. In fact, in the tb case, one creates models and chooses R based on a "best fit." From Ma on tb:

Three articles used either approximate Bayesian or exact likelihood methods, 24 articles used either a mathematical model fit with empirical data or a descriptive/regression approach on empirical data, and 29 articles used a simulation based mathematical model