Back in April 2020, the catch phrase was “flatten the curve.” The public was told that without lockdowns, hospitals would be overwhelmed with COVID-19 cases. Hospitals were not overwhelmed, and emergency facilities erected to take care of the epidemic went unused. By September, many jurisdictions that locked down had worse fatality rates per capita than jurisdictions without lockdowns. The goal posts were moved with claims that lockdowns were necessary to avoid catastrophe until vaccines were developed and distributed. By January, the winter peaks in fatalities were in decline before vaccination programs took place.
Most recently, the goalposts have been moved further with the claim that lockdowns are necessary to deal with the Delta variant. Yet, in India (see the chart below) whence the Delta variant emerged, cases and fatalities have already declined to low levels. In the UK, cases declined before the lockdowns and have slowly risen during the lockdowns. Australia seems to lock down whenever a new case is detected. The following discussion will explain why the predictions were wrong, why no government policy in some cases led to superior results than lockdown, and why new outbreaks emerge whenever lockdowns are relaxed.
The horribly inaccurate predictions, including the infamous Ferguson model, extrapolated fatality rates from hospitalized patients to the entire population, made faulty assumptions about homogeneity of risk, and overestimated growth parameters to reach predictions of apocalypse that justified lockdowns. To understand what went wrong with these predictions, we need to examine the dynamics of how respiratory viruses spread through a population.
Four phases of a viral outbreak
Phase 1 (Black) is the exponential growth phase where the rate of growth increases with the number of infected persons. Phase 2 (Brown) is the declining rate of growth phase where growth is limited by availability of susceptible hosts. Phase 3 (Yellow) is the beginning of decline where there are still susceptible hosts, but the rate of resolution of cases exceeds the rate of spread to new hosts. Phase 4 (Red) is the exponential decline phase where there are no more susceptible hosts (Herd Immunity), and a percentage of active cases resolve to either death or recovery during each time increment.
Initial models assumed the population was homogeneous with respect to the human host population. By homogeneous, it is meant that the risks of becoming infected, becoming ill and dying from COVID-19 are roughly uniform across the entire population. This assumption turned out to be wrong, but it is necessary to understand the dynamics of virus spread through a homogeneous population before one can understand the dynamics of virus spread through a stratified risk population.
Figure 1 illustrates the dynamics of a viral outbreak through a homogeneous population. For those interested in the maths, the mathematics of viral outbreak are similar to the mathematics of bacterial growth with limited nutrients. There are four phases of growth that transition one to another due to increasing number of infected hosts (cases), decreasing number of susceptible hosts, and resolution of cases to either death or recovery. For a homogeneous population, it is reasonable to assume that the percentage of cases that die will be constant over time; cases are a reasonable proxy for eventual deaths.
Phase 1 is the exponential growth phase. The virus spreads via human contact between an infected person and a susceptible person. As the virus spreads, there are more infected people to spread virus which is the basis for exponential growth. During phase 1, the number of infected people is small enough that decreasing numbers of susceptible hosts does not significantly affect the growth rate. The rate of resolution of cases also increases with the number of cases, but we can assume that the rate of spread is greater than the rate of resolution; otherwise, there would be no outbreak and the virus would disappear spontaneously from the population.
During phase 2, the decreasing number of available hosts becomes a significant brake on the rate of growth; cases continue to increase, but the rate of increase slows. During phase 3, the decreasing number of available hosts is so important that the number of human interactions between an infected person and a susceptible person is no longer greater than the resolution of cases; number of cases reaches its peak and declines. Phase 4 is what is called herd immunity. There are no more susceptible hosts, so the cases decline as they resolve into either death or recovery. This phase follows an exponential decay to zero cases.
Figure 2: COVID-19 deaths per million population from March 1, 2020 until September 1, 2020. Data values are 7 day moving average to smooth out fluctuations caused by weekly reporting of deaths. Data are from Worldometer.
Figure 2 illustrates COVID-19 mortality in Sweden from March 1, 2020 until September 1, 2020. Sweden had very little government policy. The schools were not closed. Restaurants, bars, gyms and other businesses remained opened. There were no mask mandates or official social distancing mandates. Sweden was criticized for this liberal policy, and there were many predictions of doom that did not materialize. As we shall see, Sweden did better than some jurisdictions with government lockdowns. The main features of Figure 1 based on theory can be seen in the Figure 2 real-world data. There is an easily identified exponential growth phase 1, followed by a peak in deaths, followed by a decline approximating an exponential decay to zero. Based on this data, we can infer that Sweden achieved herd immunity to the initial virus irrespective of any measurement of antibody levels. The appearance of an exponential decline to zero is a practical definition of herd immunity.
Effect of lockdown of a homogeneous population
Figure 3: . The Black curve shows the baseline case without any intervention. The Red curve shows the effect of Isolation of members of the population from other members creating a segregated population with non-homogeneous behavior. The Green curve shows the effect of restricting interactions without isolation; the number of interactions for each person is decreased, but each person can still interact. The Green curve is what is meant by “flattening the curve.”
There are two very different types of lockdowns that can be applied to a homogeneous population. One type is to segregate people from each other. This limits the spread of virus to only the members of the cell where the virus enters. There is no interaction from one cell with another, so the other cells are protected. A homogeneous population has been transformed into two groups: one group is at risk for the virus; the other has no risk. In effect this type of lockdown limits the number of available cases which scales the growth curve down in size. The peak occurs at the same time, but the magnitude of the peak is decreased.
An example of this type of lockdown would be decreasing the size of nursing homes such that fewer residents live in a greater number of homes. The other type of lockdown is restriction of interactions without segregation. This limits the rate of spread. This slows the rate of exponential growth, delays the time to reach the peak number of cases or deaths, but the area under the curve (total deaths) is unchanged. An example of this type of lockdown is restrictions on the number of interactions people can have. Closing restaurants, bars, and other businesses is an attempt to achieve this result, but whether the number of interactions decrease or are shifted to other locations is questionable. We can now examine the real-world data to see what the effects of policy were. (Note: I am not trying to predict anything as I do not know the values of the various constants in the equations. Rather I am using qualitative analysis to examine what happened in various jurisdictions and explain why the data looks the way it does.)
Comparison of mortality data of New York state and Sweden. Data values are 7-day moving average of deaths per million population. Data are from Worldometer. Blue curve shows data from Sweden. Brown curve shows data from New York.
New York state has had relatively harsh lockdowns since the beginning of the COVID-19 pandemic. Governor Cuomo has been very vocal in his criticism of other leaders who did not follow his “lead” in policy. The data show that Sweden, without any formal lockdown, had roughly 20 per cent the mortality as New York with its lockdown. Furthermore, the pattern of the data show that the New York lockdown resulted in a faster growth phase, same time to peak and similar decay pattern as Sweden. We can conclude that Sweden, without any government policy, had superior isolation of people than did New York, where government was actively trying to limit spread.
One explanation for the New York data was the policy that nursing homes could not refuse COVID-19 patients from hospitals. This led to introducing COVID-19 into a greater number of cells than occurred in Sweden, where people relied on common sense. There is no evidence from the data that the closure of schools, restaurants, or bars had any impact on the spread of COVID-19 in New York. This finding illustrates a flaw in the logic of lockdowns. It was assumed that by closing schools, restaurants, bars, and workplaces, that there would be fewer interactions between people. However, it is quite possible that people forced to stay at home will have greater interactions, but with a smaller number of people. We will return to this point after discussing the importance of stratified risk.
Figure 5: Comparison between Sweden and Texas state from March 1, 2020 until October 1, 2020. Data are 7-day moving averages. Blue curve shows data from Sweden. Brown curve shows data from Texas. L+ indicates the start of the Texas lockdown on March 19, 2020. L- indicates the start of Reopening Phase 3 in Texas on June 3, 2020.
Some jurisdictions did “flatten the curve.” My home state of Texas locked down on March 19, 2020. Restaurants, bars, gyms, and many businesses were closed. Figure 5 shows that COVID-19 mortality had a slower rate of growth in Texas compared to Sweden. Furthermore, the peak of mortality occurred later in Texas (sometime in May). Note, however, that unlike Sweden, the Texas curve did not decline to zero. Rather there was a decline to a positive asymptote or plateau. I will discuss the importance of this plateau further when discussing the dynamics of viral outbreak with a stratified population. Following relaxation of the lockdown on June 3, deaths increased in a pattern very similar in shape and magnitude to what occurred earlier in Sweden. The effect of lockdown in Texas, after the lockdown was relaxed, was a deferral of deaths rather than a prevention of deaths. Note that following the peak on this graph, deaths did not decline to zero in Texas. As a result of this “plateau of death” the total mortality in Texas has exceeded the mortality in Sweden which had no lockdown.
It would appear, therefore, that not only did lockdown fail to prevent deaths in Texas, but the lockdown may also have increased the total number of deaths due to side effects of delay. These side effects are due to stratification of risk in the population and different effects of lockdown on the different risk groups.
Stratification of Risk
We now know that the population is not homogeneous with respect to risk of death from COVID-19. The latest Centres for Disease Control, which include the recent Delta variant outbreak, show that the risk of death from COVID-19 is 600 times greater for someone 85 years of age or greater compared with someone aged 18-29. This stratification of risk requires several important changes in analysis.
Stratification of risk: In contrast to a homogeneous population, there are two groups of people with different risk of COVID-19. On the left are the young people who have a low risk of death. On the right are the elderly with a high risk of death.
We can no longer use cases as a proxy for deaths, because the percentage of elderly cases accounts for the vast majority of deaths. To simplify analysis, consider the situation where the young people on the left have zero deaths. In this situation, cases of young people contribute nothing to the death total. Rather than restricting interactions among young people, the correct strategy to minimize deaths is to increase interactions among young people, and control interactions between elderly people (segregate the elderly) and decrease entry of cases from the young population into the elderly population. An increase in interactions among young people leads to herd immunity faster, so the risk of transmission from young to elderly has a shorter duration of time.
Effect of Lockdowns of Low-Risk Population
Figure 7: Response of stratified risk population to lockdown of the low-risk group. The Black curve is the situation without lockdown. The Green curve is the situation with a long lockdown (longer than the time for cases to decline in the no lockdown case). The Bed curve is an intermediate result of a short lockdown.
Figure 7 illustrates the expected mortality curves for lockdowns of young low-risk people in a stratified risk population. The Black curve is unchanged from the homogeneous population. This curve is produced by a rapid spread in the young low-risk group leading to a pulse of high amplitude and short duration. As the durations decrease with higher amplitudes, the mortality curve looks more and more like the impulse response of an R-C network. Using signal-processing analytic techniques, as the spread through the young low-risk population becomes lower amplitude of longer duration, the mortality curve looks more like the step response of a R-C network. The Green curve illustrates such a response. Rather than having a fast rise to a sharp peak, there is a slower rise with exponential approach to a plateau. The plateau continues until susceptible people in the young low-risk group are exhausted; the curve then descends to zero consistent with herd immunity.
The Brown curve is an intermediate result from a short duration lockdown. The increase in deaths is slower than the Black curve, the peak is lower than the Black curve, the descent is to a plateau rather than zero until susceptible young, low-risk people are exhausted and herd immunity occurs. Under ideal circumstances, the areas under the curves would be equal, all consistent with the same number of young people transmitting cases to the elderly high-risk group. However, there is difficulty in maintaining precautions for interactions between the young and elderly people over long periods of time. It is possible that alert fatigue will defeat the intentions of the lockdown and more elderly people will be exposed and die.
A very conspicuous difference between the behavior of a homogeneous population and the stratified risk population is the presence of a “plateau of death.” These deaths continue at some nominal level long after the peak has occurred. This plateau is due to slow introduction of new cases into the elderly high-risk population from the young low-risk population long after the cases and deaths decline. The plateau continues until the availability of susceptible hosts among the young people are exhausted and herd immunity is achieved. These plateaus can be seen in many data sets. A very notable example is France, but we can also see this effect in India.
Figure 8: Mortality curve for Sweden from March 1, 2020 to August 11, 2021. Data are 7-day moving averages.
Figure 8 shows that even voluntary restriction of interactions among young people that slow the spread of virus through the young low-risk population can produce a plateau of death by delaying herd immunity. The response to the winter outbreak in Sweden demonstrated a slightly slower rise time during the growth phase, and a very prominent plateau of death prior to the eventual exponential decline to zero after herd immunity was achieved.
Think of it this way. When I was a young boy, the community response to a case of mumps or measles was to have a neighborhood party and put all the susceptible children in the same room as the infected child. All the children got sick at the same time, and the outbreak was over in 3-4 days.
Why, if herd immunity was achieved in Sweden in the summer of 2020, was there a winter outbreak? The virus adapts to its environment. The virus mutates over time. If the environment selects against certain configurations, mutations that sufficiently change the configuration to fool the human immune defenses grant a survival advantage and the new strain quickly becomes the dominant strain. The winter outbreak seen throughout the world was due to new strains. The current outbreak is due to the Delta variant which has emerged due to immunity against wild type conferred by either vaccine or recovery from illness.
This adaptation is why we have not eliminated influenza despite 100 years of trying. We will not eliminate COVID. Which brings the discussion to the situation in Australia.
What about Australia?
Figure 9: New COVID-19 cases in Australia from March 1, 2020 until August 11, 2021. Data are 7-day moving averages. The graphic illustrates cases, because it is difficult to see the current spike due to the Delta variant if deaths are plotted as the mortality rate is so low.
The policy in Australia has been to lock down whenever a few cases are detected. The mortality rate from COVID-19 in Australia has been very low compared with other nations or US states. However, every time Australia relaxes the lockdown, there is a risk of a new outbreak. This risk will continue until herd immunity has been achieved. As has been the case everywhere else in the world, herd immunity will be temporary. Jurisdictions with extensive mass vaccination programs including Israel have seen outbreaks in cases and the emergence of deaths from Delta variant. Sweden has provided an example of what to expect if a nation learns to live with COVID-19. Sweden appears to be doing just fine.
Australia has a choice to make: either accept that some people, mostly over the age of 80, will die each year from COVID-19; or become permanent inmates in a maximum security prison. Australia was founded as a prison colony. Do Australians wish to become once again a nation of prisoners?
Dr Gilbert Berdine MD is an associate professor of internal medicine at the Texas Tech University Health Sciences Center (TTUHSC) and a faculty affiliate with the Free Market Institute. Dr Berdine earned his undergraduate science degree in chemistry and life sciences from the Massachusetts Institute of Technology in Boston and his graduate medical degree from Harvard University School of Medicine in Boston. He completed both his residency in internal medicine and fellowship in pulmonary diseases at Brigham and Women’s Hospital in Boston. He writes for both the American Institute for Economic Research and Mises Institute and wrote for Quadrant Online on vaping.