So this model shows that a population may reach natural HIT (herd immunity threshold) once 20 percent of the population is immune...(or at least at much lower levels than with vaccine immunity.
https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v3.full.pdf
The herd immunity threshold
Individual variation in risk of acquiring infection is under selection by the force of infection, whether individual differences are due to biological susceptibility, physical exposure, or a 10 combination of the two traits. Selection results in the removal of the most at-risk individuals from the susceptible pool as they become infected and eventually recover (some die). This selective acquisition of infection and immunity results simultaneously in decelerated epidemic growth and accelerated induction of immunity in the population. The herd immunity threshold (HIT) defines the percentage of the population that needs to be immune to reverse epidemic 15 growth and prevent future waves. Figure 3 shows the expected downward trends in the HIT for SARS-CoV-2 as the coefficients of variation of the gamma distributed susceptibility or exposure are increased between 0 and 4 (to assess robustness to changing the type of distribution see Figure S22 for equivalent plots with lognormal distributions). While herd immunity is expected to require 60-70% of a homogeneous population to be immune given an �! between 2.5 and 3, 20 these percentages drop to the range 10-20% for CVs between 2 and 4. Therefore, a critically important question is: how variable are humans in their susceptibility and exposure to SARSCoV-2? Hitherto, there is no definite answer to this question.
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Discussion
The concept of herd immunity is most commonly used in the design of vaccination programs (12, 13). Defining the percentage of the population that must be immune to cause infection incidences to decline, herd immunity thresholds constitute convenient targets for vaccination coverage. In 25 idealized scenarios of vaccines delivered at random and individuals mixing at random, herd immunity thresholds are given by a simple formula (1 − 1⁄�!) which, in the case of SARSCoV-2, suggests that 60-70% of the population would need be immunized to halt spread considering estimates of �! between 2.5 and 3.
A crucial caveat in exporting these calculations to immunization by natural infection is that natural infection does not occur at random. 30
Individuals who are more susceptible or more exposed are more prone to be infected and become immune, which lowers the threshold (14). In our model, the herd immunity threshold declines sharply when coefficients of variation increase from 0 to 2 and remains below 20% for more variable populations. The amplitude of the decline depends on what property is heterogeneous and how it is distributed but the downwards trend is robust (Figures 3 and S22)
So what the study and charts say is that if you keep the large majority of your population locked up at home and only allow a small percentage of your population out (the connectivity factor CV) --- then a large portion of the population that you allow out and about will be immune after getting sick. This, of course, is based on the premise that 80% of your communities is strictly locked-up at home and less than 20% is moving around as essential workers. In this manner only 20% of your overall population needs to be immune to provide "herd Immunity" -- but it still means that 80% of your population needs to be locked-down forever.
Any reasonable scientist knows that the minimum percentage to achieve herd immunity for a infectious disease is 50% across an entire community with no mitigation... this is easily proved with mathematical models. For most diseases the minimum level is above 70%.