Findings based on a SIR (Susceptible, Infectious or Recovered) Model of Infection Dynamics, commonly used to determine infection scenarios, including COVID-19, and presented at the Artificial Intelligence and the Coronavirus workshop at the International Conference on Artificial Intelligence in Medicine, say that New York and California may have reached herd immunity.

In late June, New York State was close to reaching herd immunity, according to the SIR model, which is defined by a disease reproduction number of less than one. Considering a steady decrease in reported mortality rates since then, the basic reproduction number under the current social distancing restrictions was 1.14. The basic reproduction number is the average amount of secondary infections an infected person will cause in a completely susceptible population.

At that time, New York had approximately 400,000 confirmed cases, implying 2.4 million (6x more) actual infections based on the results of serological tests conducted in the state.  The model found similar results for both Israel and California, with California reaching herd immunity around July 15th, with slightly more than 10% of their population (4.05 million) being infected.  Their basic reproduction number, R0, was under current restrictions of 1.1. 

If the current restrictions are maintained and there are no unusual spreading events, at the end of August or the beginning of September there should have been enough people with antibodies in order to achieve herd immunity, the model states. 

That's no reason to be overconfident. Though the real danger rate is only .03, 60 percent of those admitted to intensive care units will die - three times the average 20 percent mortality among all patients admitted to ICUs. 

The model was based on the COVID-19 attributed deaths reported by the Israeli Ministry of Health on a daily basis and an estimation of the total number of infected people based on published results of serological tests rather than just on confirmed cases. 

Obviously you cannot know the actual number of cases of infection unless entire populations are tested every day.