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COVID-19: U.S. may reach the benefits of herd immunity sooner than originally thought

Rådgivning om selskapsrisiko|Forsikringsrådgivning og teknologi|Reassuranse
COVID 19 Coronavirus

By Dave Ingram | August 20, 2020

The benefits of herd immunity from COVID-19 sound attractive. The pandemic starts to die off “naturally” and the number of new cases declines. But the cost seems very high.

The most common situation that is cited for herd immunity regarding COVID-19 is when 60% of the population has been infected.1 But this calculation reflects what was happening before countermeasures to slow the spread of the virus were adopted. That situation (no countermeasures) may be true for the common cold or for a herd of cattle, but our experience so far with COVID-19 is that many people are very likely to actively avoid infection and those efforts will increase as the infection rate rises and infections become more widespread.

The following thought experiment describes how it is quite possible to achieve the benefits of herd immunity at different — much lower — levels of total infections when you reflect continuing levels of mitigation activities as personal or government-imposed countermeasures rather than going immediately back to normal.

“We are still nowhere near back to normal in our daily behavior,” said Virginia Pitzer, a mathematical epidemiologist at the Yale School of Public Health. “To think that we can just stop doing all that and go back to normal and not see a rise in cases I think is wrong, is incorrect.”2

The U.S., the country with the highest level of COVID-19 infections, still has a long way to go before 60% of the population has been infected. Cumulative infections at the end of July were a little less than 1.4% of the population. A 60% infection rate is over 40 times that level. But in the following projections, with continuing mitigation behaviors, you will see that the pandemic would die off at levels of infection substantially below 60%.

Daily new infection rate

First, let’s look at the rate at which infections are appearing in the population. For this, we will focus on a new measure that I will call the daily new infections rate (NIR). To calculate this factor, you need the number of new cases for the past 15 days. The NIR is calculated as the most recent day’s new cases divided by the sum of the prior 14 days’ new cases.3

U.S. new infections

The sum of new infections from June 16 to June 29 is 459,481. The NIR for June 30 is 43,644/459,481 = 9.5%.
Date Number of infections
16-Jun 18,577
17-Jun 27,975
18-Jun 23,251
19-Jun 23,138
20-Jun 36,908
21-Jun 32,411
22-Jun 27,616
23-Jun 26,643
24-Jun 34,327
25-Jun 37,667
26-Jun 40,588
27-Jun 44,602
28-Jun 44,703
29-Jun 41,075
30-Jun 43,644

New infection rate values

The NIR for the last seven days of July for the U.S. in total4
Date NIR
24-Jul 8.6%
25-Jul 7.1%
26-Jul 6.0%
27-Jul 6.1%
28-Jul 6.7%
29-Jul 8.1%
30-Jul 7.3%
31-Jul 8.6%

Over the entire month of July, the NIR averaged 8.2%, and that was also the average for June. For the month of May the average was 6.7%. The NIR changes as community safety practices change and as the proportion of those immune increases. If the number of new cases is the same every day, the NIR is 1/14 or 7.1%.

You could imagine that there are several things that would influence the rate of growth in new infections, including:

  1. The underlying transmissibility of the disease
  2. The frequency and duration of close interpersonal contact in the population
  3. Prevalence of compliance with measures to reduce transmission of the disease such as masks and other personal protective equipment (PPE), handwashing and sanitizing
  4. Reporting lags, errors and changes in the volume of testing

We suggest that the current NIR reflects the impact on transmission of infections that results from all the recent countermeasure practices for (2) and (3). Even if all four factors were to remain constant, there would still be some variations from day to day, driven by other factors that we do not know yet, or simply by random chance.

Three projections

If we use NIR as the primary factor to drive a simple projection of the course of the pandemic, we can learn what might happen to the future spread of the disease taking into account the actual situation and experience of that population regarding disease transmission. The projection can presume that the impact of the practices stays the same or that they get better or worse by using different values of NIR over time.

Although we cannot show the impact of any specific actions, we can show a future course of the pandemic assuming a particular NIR that is consistent with the levels of mitigation practices that are consistent with some period of time.

There is one additional factor that is fundamental to projecting the course of a pandemic: the degree of immunity within the population. Influenza pandemics are often repetitions of strains of the virus that went through the population sometime in the past. People who have previously been infected by a specific strain and recovered are often immune to future infections from the same strain. It is ultimately the growing immunity in a population that will cause the curve to bend and finally flatten.

A simple model of the future course of a pandemic can then be built using just the following:

  • The total number of past infections5
  • The new cases from the past 14 days
  • Assumptions for the NIR
  • The case fatality rate (CFR)

We will use an assumption of a 3.4% trending to 3% CFR here. The rate at the end of July for the U.S. was 3.4%, and it had trended downward steadily from 5% at the end of June.

To produce illustrative projections using this approach, we will choose three different courses for future NIR. First, consider the history from May to mid-July:

From May to July, new cases increased by 25,000
U.S. new infection rate from May 1, 2020 to July 30, 2020 – moving seven-day average

You can see from this graph, that NIR was not at all stable in June and July for the U.S. The run up of NIR from mid-June to early July is likely driven by abrupt changes in mitigation practices throughout the U.S. as states ended many of the restrictions that were in place from mid-March. The falling NIR from the end of June through the end of July reflects changes in individual and government mitigation practices in response to the increased spread of the pandemic.

The three illustrations that are used for this thought experiment are 6%, 8% and 10%. The first two bracket the experience through mid-June, and 10% to show something at the level of the late June experience. It is very important to note that these are projections not predictions. Like the message of Dickens’ “Ghost of Christmas Yet to Come,” these projections may happen, but we have the power to change our future, in this case by changing our community safety practices.

At 10% NIR, cases peak and start to decline in mid-October 2020
10% base new infection rate (without immunizations) Projected total COVID-19 cases
At 10% NIR, cases peak and start to decline in mid-October 2020
10% base new infection rate (without immunizations) Projected new COVID-19 cases

With a 10% NIR, the pandemic reaches a peak of new cases and starts to decline in mid-October. At the peak, the daily infection rate passes 2 million. This projection is highly unrealistic because it does not reflect any changes to the NIR or the CFR as the medical systems get overwhelmed.

In the U.S., hospitalizations have averaged around 6% of infections through the end of June, and there are approximately 1 million hospital beds in the U.S. in total. Applying that to the projected infections with the above 10% NIR assumptions, the number of needed hospitalizations will exceed the number of hospital beds before the end of September and remain above 1 million for about two months.

Additionally, under this scenario, deaths reach a level that Americans and our political leadership will find unacceptable. At the end of July, U.S. deaths from COVID-19 were about 150,000. Under the 10% projection, cumulative deaths would double by late August and double again by mid-September, at more than half a million deaths. It seems highly unlikely that this would happen without some measures to increase mitigation activities and thereby drive the NIR down substantially below 10%.

At 8% NIR, cases peak and start to decline end of January 2021
8% base new infection rate (without immunizations) Projected total COVID-19 cases
At 8% NIR, cases peak and start to decline end of January 2021
8% base new infection rate (without immunizations) Projected new COVID-19 cases

With the 8% NIR, the pandemic grows slowly throughout the one-year projection period. The number of new cases peaks at the end of January and slowly declines. This is likely to be an achievable scenario, as the U.S. experience was below 8% from early May to mid-June and averaged just 8.2% in June and July.

In this scenario, estimated hospitalizations peak at under 250,000, which is well below the 1 million total hospital beds in the U.S. Under this scenario, deaths reach 1 million by year-end, which may also lead to a significant reaction to reduce the spread of infections.

At 6% NIR, cases fall throughout the projection period
6% base new infection rate (without immunizations) Projected total COVID-19 cases
At 6% NIR, cases fall throughout the projection period
6% base new infection rate (without immunizations) Projected new COVID-19 cases

In the 6% NIR projection, the new cases fall throughout the projection period. This projection reflects an NIR that is lower than what was experienced in the U.S. for 45 of the 61 days in May and June. In fact, these low values may be the result of errors in reporting.

With the pandemic receding throughout the 6% NIR projection, hospitalizations remain low in total for the U.S. and deaths top out at 210,000.

It helps to look at the three together. This shows that there is a stark difference between the outcomes with future scenarios where the NIR is at different levels within the range that we have experienced within the past two months.

Graph shows 10%, 8% and 6% new infection rates
Projected total U.S. COVID-19 cases at 10%, 8% and 6% base new infection rates

Benefits of herd immunity

The benefits of herd immunity start when the new cases curve reaches a peak and starts to turn down. These three projections all show the U.S. achieving the benefits of herd immunity. None gets to the often-reported 60% infection rate. The benefits of herd immunity are achieved at a 27% infection rate for the 10% NIR projection, at 11% infection rate for the 8%, and it is present from the start of the 6% projection. But while the benefits of herd immunity are technically achieved at those cumulative infection levels, new infections are reduced after that point, but can continue for months.

Because the NIR is defined as the new cases divided by the sum of the prior 14 days’ new cases, each infection runs through the model as an active case causing new infections for 14 days. In the 10% projection, we apply that 10% rate to each of the active cases for those 14 days, which results in 1.4 future new cases from each of today’s cases. At 8%, there are 1.12 future new cases from each of today’s new cases. Finally, at 6% NIR, there are only 0.84 new cases from each of today’s new cases, resulting in a decline.

When the number of future new cases from today’s cases decreases to 1.00, the new case curve peaks and the benefits of herd immunity come into play. Solving for that result, we find that an NIR of 7.14% results in the benefits of herd immunity.

Right now, the level of immunity in the U.S. and world population is very low. The U.S. is the country with the highest percentage of current and prior COVID-19 cases, and the level of immunity in the U.S. is about 1.03%.

But the three projections show that the level of immunity needed to reach the benefits of herd immunity is different at different levels of the NIR.

An important detail is that all of the above statements about the benefits of herd immunity are based on the assumption used here that whatever COVID-19 safety practices that are driving the initial level of NIR in terms of limiting the frequency and duration of close interpersonal contact and prevalence of measures to reduce transmission of the disease, such as masks and other PPE, handwashing and sanitizing, are continued into the future including after the benefits of herd immunity are reached.

Safety practices did not continue in the U.S. after reaching the benefits of herd immunity in May. In May and June, the U.S. had experienced an NIR below 7.14% but the announcement that a plateau had been reached seemed to automatically trigger a relaxation of the COVID-19 safety practices and the NIR shot back up to over 9%.

Impact of vaccine

Herd immunity can be achieved by either surviving infection or vaccination. If the earliest possible date for a new vaccine is January 1, 2021, then the vaccine will not help toward achieving the benefits of herd immunity in either the 6% or the 10% example. In the 8% projection, the benefits of herd immunity are reached in February, so a vaccine that is widely available in January could speed up the arrival of the onset of the benefits of herd immunity by a few weeks.

In addition, a vaccine can be an important factor to counteract the impact of the relaxation of COVID-19 safety practices that would likely occur once the benefits of herd immunity are reached.

Second wave

A second wave in the U.S. (or any other country) is possible if, for example, the following conditions occur:

  • The first wave reaches the benefits of herd immunity and infections drop slowly to a very low level or even zero.
  • The pandemic does not reach the benefits of herd immunity level in some other country, so there are a large number of actively infected people from other parts of the world who can bring the disease back into the U.S.
  • The people of the U.S. have abandoned most efforts to limit interpersonal contact or to reduce the potential for transmission of an infection and are slow to re-adopt such measures when there is evidence of new infections.

The final item above will mean a much higher NIR for a time, which means that even with the amount of immunity from the first wave of infections, active infections will grow.

This is the scenario where the vaccine would have the most significant impact. If a large fraction of the population who were not infected in the first wave can get a vaccine, then the population could have sufficient immunity to make a second wave short-lived.

As these projections show, we will achieve the benefits of herd immunity. But there is a wide range of possible pandemic experiences on the way.

An earlier version appeared in Willis Towers Watson Insights on July 29, 2020.


1 That value is determined from the 2.5 R0 value that was the first published estimate of R0 in Wuhan (Majumber & Mandl, 2020). If 100 infected people pass the disease along to 250 others and 60% of them are immune (150), then there will be only 100 new infections. This means that the number of infected people remains flat at 60% and starts to fall as new infections push the total infection rate over 60%.

2 “What if ‘Herd Immunity’ Is Closer Than Scientists Thought?” New York Times, August 17, 2020

3 The daily NIR is a measure of the new infections in a day as a percentage of the active infections, while the common term, infection rate, is the total infections over time as a percent of the total population. Since the recordkeeping for active infections is weak, we instead use the new infections for the prior 14 days. Fourteen is chosen because it is the suggested length of time to quarantine after potential exposure.

4 New case values obtained from the Our World in Data website.

5 Including the current and any past experiences with the pandemic virus. In the current situation with COVID-19, there is no past experience. This is the first time, at least in living memory, that humanity has seen this virus.


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