According to www.mayoclinic.org "Experts estimate that in the U.S., 70% of the population - more than 200 million people - would have to recover from COVID-18 to halt the epidemic." Another source www.webmd.com says "50% to 67% of the population would need to be resistant before herd immunity kicks in and the infection rates start to go down." Thus I had not thought about detecting herd immunity.
For California, 8/10/2020, LA county has a high (compared to other counties, only Marin is higher) confirmed cases per million of population 21.5K/1M or ~2%. Even that is way low compared to over 50% for herd immunity. For more information on LA etc see https://confluence.slac.stanford.edu/display/IEPM/Covid-19+California+coastal+counties.
As of 8/13/202 for the US the state with the largest confirmed cases/million population is Delaware with 29906.94911 ~ 3%.
Adding in asymptomatic cases might help but would seem to have large error bars (see https://www.cebm.net/covid-19/covid-19-what-proportion-are-asymptomatic/). A parameter that might be useful for adding in asymptomatic cases might be the following from: https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html
Percentage of infections that are asymptomatic: The percentage of persons who are infected with SARS-CoV-2 but never show symptoms of disease. Asymptomatic cases are challenging to identify because individuals do not know they are infected unless they are tested, which is typically only done systematically as a part of a scientific study.
The CDC 7/20/20, in a series of Scenarios, indicate the best estimate is 40%. Thus we might increase the number of confirmed cases by 40%. For LA county increasing the 21.5K by 1.4 times yields 30.2K or 30,200/1,000,000 = 3%. This is still very low. For Delaware adding 40% yields ~ 4.2%.
Professor Gomes of the University of Strathclyde in Glasgow produced a model suggesting herd immunity may be as low as 10-20%, see https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v3.
Dr. Manoj Jain on infectious disease physician at the Rollins School of Public Health says "By definition, herd immunity means we can let our guard down, that we can go life as usual. That is not the case in our declining numbers. Our numbers are declining in part because we are masking and distancing. This lowers our transmission number, which in turn lowers the percent of the population required to achieve 'herd immunity'... If we stop that, then the population percent required or herd immunity will go up."