Herd immunity from Covid-19 sounds attractive. The pandemic starts to die off "naturally". 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.
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The following describes how it is quite possible to achieve herd immunity at different – and much lower – levels of total infections.
The US, the country with the very highest level of Covid-19 infections, 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.
New infection rate
First, let's take a look at the rate at which infections are appearing in the population. For this, we will focus on a slightly new measure that I will call the new infection 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.
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| | New Infections |
| 16 June | 18,577 |
| 17 June | 27,975 |
| 18 June | 23,251 |
| 19 June | 23,138 |
| 20 June | 36,908 |
| 21 June | 32,411 |
| 22 June | 27,616 |
| 23 June | 26,643 |
| 24 June | 34,327 |
| 25 June | 37,667 |
| 26 June | 40,588 |
| 27 June | 44,602 |
| 28 June | 44,703 |
| 29 June | 41,075 |
| 30 June | 43,644
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The sum of new infections from 16 June to 29 June is 459,481. The NIR for 30 June is 43,644 / 459,481 x 100 = 9.5%.
Here are the NIR values for the last seven days of July for the US in total.
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| | NIR |
| 24 July | 8.6% |
| 25 July | 7.1% |
| 26 July | 6.0% |
| 27 July | 6.1% |
| 28 July | 6.7% |
| 29 July | 8.1% |
| 30 July | 7.3% |
| 31 July | 8.6% |
Over the entire month of July, the NIR averaged 8.2% – the same as in June. For the month of May, the average was 6.7%.
You could imagine there are a number of things that would make the NIR change, including (1) the underlying transmissibility of the disease, (2) the frequency and duration of close interpersonal contact in the population, (3) prevalence of measures to reduce transmission of the disease such as masks and other personal protective equipment, handwashing and sanitising, (4) reporting lags and errors.
We suggest the current NIR reflects the impact on transmission of infections that results from all of the recent 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
The NIR can be used as the primary factor to drive a projection of the course of the pandemic. Using the NIR, we can project the future spread of the disease taking into account the actual situation and experience of that population regarding diseasetransmission. The projection can presume that practices stay the same or that they get better or worse by using different values of NIR.
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 and recovered are often immune to future infections. It is ultimately the growing immunity in a population that will cause the curve to bend and ultimately flatten.
A simple model of the future course of a pandemic can then be built using just (a) the total number of past infections
4 (b) the new cases from the past 14 days and assumptions for the (c) NIR and (d) the case fatality rate (CFR).
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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:
The three illustrations will use 6% and 8%, which 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 Future, these projections may happen, but we have the power to change our future, in this case by changing our community safety practices.
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 US, hospitalisations have averaged around 6% of infections through the end of June and there are approximately 1 million hospital beds in the US in total. Applying that to the projected infections with the above 10% NIR assumptions, the number of needed hospitalisations will exceed the number of hospital beds before the end of September and remain above 1 million for about two months.
In addition, under this scenario, deaths reach a level that Americans and our political leadership will find unacceptable. At the end of July, US 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 driving the NIR down substantially below 10%.
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 US experience was below 8% from early May to mid-June and averaged just 8.2% in June and July.
In this scenario, hospitalisations peak at under 250,000 which is well below the 1 million total hospital beds in the US. Under this scenario, deaths may also lead to a significant reaction to reduce the spread of infections, reaching 1 million by year end.
In the 6% NIR projection, the new cases fall throughout the projection period. This projection reflects a NIR that is lower than what was experienced in the US 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, hospitalisations remain low in total for the US and deaths top out at 210,000.
It helps to look at the three together. It shows 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.
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