What does the other side of the curve look like?

In last few months a whole new set of terms have entered everyday use. There is the pandemic curve, social distancing, the need to flatten the curve, inflection points, an apex, surges, surge capacity and herd immunity. The curve was perhaps most simply expressed by Dr. Anthony Fauci early on in this crisis when he said “Its going to get worse before it gets better.”

The Curve:

There is a very cool article from the Washington Post. It includes an infection disease outbreak simulator (Figure 1). There are dots moving around the screen, at first they are all “healthy”, except one dot who is infected. As the dots move around and the infected one bumps into healthy dots, the healthy dots become infected. Before your very eyes you watch the number of infections grow to a peak (brown area in graph in figure 1). Then gradually some of the infected dots “get better” and turn purple. They can no longer get infected because they have become immune to the disease. So, when they bump into an infected dot, nothing happens.  No dots die in this simulation, they all eventually recover.  The brown part of the graph below is your infectious disease curve.  It starts out slowly, when only a few people have the disease, but gradually as the disease spreads and more sick dots are bouncing about, the infection rate grows more rapidly, the slope of the curve gets steeper. But as the time goes by, there start to be a growing number of dots that have recovered and cannot be re-infected. This growing number of immune dots eventually cause an inflection point, where the slope goes from constantly getting steeper, to switching to a transition where it starts getting less and less steep, until it hits the Apex of the infection, the point at which the most number of dots are sick.

Figure 1: Epidemic Simulator

Herd Immunity:

This Washington Post simulation illustrates the concept of herd immunity. The idea is that when a sufficient part of the “herd” or population is immune from an infectious disease, the amount of that disease in the population will naturally go into decline. The simulation represents an over simplification. In the simulation, all the dots eventually get sick, and eventually recover. But in the real world, effective herd immunity does not require that the entire herd be immune to ensure protection of the whole community. Exactly how many members of the herd need immunity depends on a lot of things, foremost is how infectious the disease is.

R naught:

Epidemiologists use the term R naught or R0 as a measure of how infectious a disease can be. R naught is the average number of new cases that each existing case will cause.  Diseases with a high R naught will spread faster than diseases with a lower R naught. An outbreak of a disease with an R naught below one, will quickly end all by itself as on average, each new case will generate less than one new case. Measles is a very infectious disease. R naught for measles is estimated to be between 12 and 18. That is, in a population where everyone is susceptible to measles, each new case will infect 12 to 18 new people.  The estimates for Coronavirus R naught range from 1.5 to 3.5. The actual R naught depends on a lot of factors and can vary based on things like population density and social customs. The effective R naught can also be influenced by social distancing. For example, if the true R naught were 1.5 under “normal” circumstances, and then you introduce social distancing that cut in half the number of social interactions that the average person has, you would expect the effective R naught to go from 1.5 to .75. That would make it less than 1, and we would expect to see the infection rate to decline.  However, if the initial R naught was 3.5, and social distancing cuts in half the number of social interactions that can result in infection, the effective R naught would be 1.75, still high enough to cause outbreak to grow. R naught also assumes that the entire population is susceptible to infection. If some people are immune, either because they have had the disease or have been vaccinated, the actual number of new cases caused be each infection can be much lower. So with measles, which is very infectious, public health experts estimate that if 95% of the population is vaccinated against measles, then the effective R naught is below 1, and any outbreak is unlikely to spread beyond a few cases.  Less infectious diseases require a lower vaccination rate to effectively keep the disease under control.  Sadly, we currently have no vaccine for coronavirus, but it is widely assumed that people who have recovered from coronavirus have immunity for at least some period of time.  So, how many people need to get corona virus and recover to reduce the spread of the outbreak?  It depends on the R naught. If the R naught is something like 1.5, then once over 1/3 of the population has had the disease, than over 1/3 of the people an infected person would encounter would be immune from the disease, which would means the effective R naught would be below 1 and the outbreak would go into a decline.  Estimates vary but one estimate says that left on checked, the coronavirus might infect 60% of the world’s population. So, unlike the simulation where the infection ends with 100% infection, coronavirus infection would drastically decline once 60% of a community had been infected. For the United States that would mean close to 200 million people being infected with the coronavirus, before herd immunity would end the epidemic. Not an exciting prospect.  

If coronavirus was not deadly to a small percentage of the population, one approach would be to simply let it rip through the population until sufficient herd immunity was achieved to end the outbreak. Many of these graphs showing infection curves that have appeared in the media in recent weeks, including figure 2 from the US Coronavirus Task force illustrate a curve where no social distancing/ protective measure have been taken side by side with a curve that reflects the effect of social distancing/protective measures.

Figure 2: Presented (date) at US Conrona Virus Task Force

In this simplified graph the red curve represents unchecked outbreak in red, while the blue curve shows the impact of social distancing. In both cases the infection eventually goes into decline because of growing herd immunity.

Enter Flattening the Curve:

Most western nations failed to contain the initial outbreak. Containment consists of careful testing, tracing of contacts, quarantine and isolation, through this process it is possible to “stop the chain on infection”. In effect you are aggressively managing the first few cases in a way that greatly reduced the effective R naught. Once the option for initial containment had been lost public health experts in the west began talking about “mitigation” and “flattening the curve”. This idea is also illustrated in the US coronavirus task force graph – figure 2.  The idea here is that there is a limit to the capacity of each nation’s health care system to take care of the people who become very ill from corona virus. If we can “flatten the curve” of the outbreak, we can keep the total number of seriously ill cases within the capacity of the health care system.  As we know, the infection curve is influenced by the effective R naught. Social distancing can slow the speed of the infection. Doing so will likely elongate the curve as seen in the example above. In this scenario, the total number of cases is similar in both curves. Theoretically it is a little smaller under the flattened curve because the combination of social distancing and growing herd immunity would cause the outbreak decline rapidly without infecting quite as many people as the “Without protective measures” curve. But in both curves we expect something close to 60% of the population becoming infected.

Health Care System Capacity:

Though figure 2 seems reassuring, a more quantitative analysis performed by the Imperial College of London paints a more depressing picture (figure 3 A & B). Though the numbers are based on UK data and their National Health Service (NHS) capacities, per capita US health care capacity is not massively larger than that in the UK. The horizontal red line represents UK Surge critical care bed capacity, while the other lines show the need for critical care beds under various levels of social distancing.  The duration of social distancing in the graph below is indicated by the shaded area, and run for 5 months. On this graph we can see that it will take much more than just chopping a little off the top of the curve, we need to cut the curve at its ankles. In fact to actually see how the various levels of social distancing interact with the health care capacity you need to look at the close-up of graph shown in figure 3 B. If the UK can keep infection levels at or below the capacity of their health care system to manage the severe cases, it will take many months, perhaps years to develop significant herd immunity. And with coronavirus we do not know how long that immunity will last.

Figure 3: Imperial College of London Projections for UK

The United States has slightly more critical care beds per capita than the UK, but the difference is like cutting the curve either above or below the ankle. The implications of this are clearly shown in figure 3B. With extensive social distancing we can keep the demand of critical care beds within system capacity. Moderate social distancing will result in a demand for critical car beds about double the existing capacity. In both cases though, once social distancing is ended, we would face spikes in infection very similar in scale to not having done any social distancing.  This is because very little herd immunity would have been created. Looking at the outbreak in Massachusetts, Governor Baker has reported that public health experts there estimate that once the initial surge is over, somewhere be 0.7 and 2.5 percent of the population will have been infected.  This is not nearly enough to propel the steady decline of infections based on herd immunity.  This means once the current crisis is over, we will remain in a situation where new spikes are likely, especially if we loosen social distancing.

Whats the other side of the curve look like?

I believe that it is quite likely that the other side of the curve will look nothing like the smooth downward slope of the US Coronavirus task force (figure 2), but rather more like the orange line in figure 3 B. Where we will see small declines and rises for as long as we keep social distancing in place.  One possible hit of what the other side of the curve can be seen in Italy’s case reports. The data in figure 4 from the web-site https:/worldometer/coronavirus we can see a peak in new cases on March 21st. But after that there is no a downward slope symmetrical to the upward one. There does appear to be a downward trend, but the road looks bumpy. Fourteen days after the peak there are still between over 4,000 new cases per day. Fourteen days before the peak there were only 1,200 new cases. Italy’s social distancing guidelines are more extreme than most of those in place in the United States. So it would be reasonable to expect our ride to be even bumpier.

Figure 4: Worldometer Website 4/5/2020

What Next:

In the United States both Federal and state officials have been projecting a surge in cases followed by some sort of markedly improved situation. We have repeatedly heard that the next week or two are going to be bad. But we should be prepared for the notion that the weeks after that may only be marginally better, and social distancing will need to continue to prevent the outbreak from going to new heights.

Of course the long term solution that the world is awaiting for is an effective vaccine. Dr. Fauci from the National Institutes of Health has repeatedly told us, that is 12 to 18 months away in the best of circumstances. Though sort of a vaccine there are not magic bullets. But some of the things that our leaders should be considering include:

  • Effective Leveraging of Limited Herd Immunity
  • Allowing a higher rate of infection while somehow shielding the Elderly and high risk
  • Find a theraputic treatment, and allow a higher rate of infection
  • Re-Attempt Containment

Effective Use limited herd immunity:

Even though we will not have a sufficient number of people recovered from the disease and who are therefor immune, we will soon have thousand of people who have recovered from Coronavirus. These people could be strategically used to “multiple” the impact of their immunity.  The idea here would be to place people with immunity in the positions where transmission is most likely to occur. This of course includes front-line positions like first responders and health care staff. But it also includes positions like cashiers, baristas, and uber drivers. Medical staff with immunity would also be ideal staff to work in nursing homes and senior living centers, as it would greatly reduce the chance that staff could introduce the virus into dense high risk settings.

To use immunity status rather than the free market to control who does what job, would be a highly unusual step for our nation. But this crises calls for unusual action. This strategy of placing immune workers in our community in key human interface locations in our society would be greatly enhanced by having a fast, cheap and reliable anti-body test that would indicate who has had the disease and is therefor immune.

If successful, this strategy might allow us to loosen some social distancing restrictions while we wait for a vaccine.

Sheilding the Elderly:

If it were possible to provide effective special protection for the elderly and other high risk individuals, it would decrease the need to keep the overall infection rate low, which is necessary to keep the hospital systems from being overwhelmed. As most people have mild cases, if we could allow the infection rate to be high in the young and healthy population, we could more quickly, accumulate herd immunity. In an ironic twist, this this might actually entail something like young people having “coronavirus parties”. The idea of intentionally spreading an infection may sound peculiar. However, prior to the development of a chicken pox vaccine, it was not uncommon for parents to organize Chicken Pox parties for young children, when a neighborhood child became infected. The motivation was somewhat different. Chicken pox is substantially less severe in young children and once infected, most people have lifetime immunity. So ensuring your child got chicken pox when they were young protected them from getting it when they were older and the infection was more severe and dangerous.

The initial response of the UK government was criticized for pursuing a herd immunity approach when it failed to close schools, restaurants and bars but recommended strong stay at home advice for the elderly. The government denied those accusations, and eventually fell in line with the rest of Europe and increased social distancing by closing schools, restaurants and bars. Sweden has also pursued a strategy of minimal social distancing, though it appears this may change soon.

A strategy of allowing a substantial number of people to be infected and thereby develop herd immunity is politically un-popular because it would likely mean large number of deaths among the vulnerable population, as well as a smaller number of younger, apparently healthy people. But we had mechanism to protect the elderly and vulnerable, it might be much better than limping along for 12 to 18 months with a persistent on-going outbreak and deaths while we wait for a vaccine.

Find A Theraputic:

Similar to shielding the elderly and vulnerable, if a treatment for those that become seriously ill could be found that substantially reduced the death rate among the hospitalized population, it would become possible to allow a higher rate of infection in the general population and thereby achieve herd immunity faster. Now when people become severly ill from the virus they require intensive care treatment. They often end up needing ventilators which are in short supply. Non Coronavirus patients needing ventilators using need them for a few days. One study in the State of Washington found that covid-19 patients have a median of 10 days on a ventilator. If a treatment were available that could be used in hospital that got people better faster, reduced the need for long term ventilation, and greatly reduced mortality among hospitalized patients, the capacity of our medical system to handle those who become seriously ill would be greatly increased. Which would mean we could reduce social distancing allowing for a faster spread of the virus, without increasing deaths, which would mean faster accumulation of herd immunity.

Re-Attempt Containment:

One option that does not rely on herd immunity, yet could provide protection while we wait for a vaccine is Containment. Containment is usually used at the initial outbreak of an infectious disease. The basic idea is to keep track of and manage all the individuals who are infected in a way to prevent those people from infecting others. It relies on traditional epidemiology using aggressive testing, tracing the contacts of positive individuals and isolating the infected and the exposed to break the chain of infection.

In general western nations completely failed at effective containment. This happened for a variety of reasons including hubris, lack of preparedness, insufficient funding and staff, problems getting testing in place, failing to perform surveillance testing to look for early silent hot spots, and probably a lack of will to ask for or impose the necessary restrictions on individuals to make containment effective.

Looking at western nations one might conclude that containment was impossible. Like the US, most countries were still struggling with getting testing off the ground at the point when such a strategy was most easily implemented. The outbreak quickly sneaked past ports and airports and was spreading wild in the community before testing systems were really available. However, three Asian nations have shown considerable success at containment.  Singapore, Taiwan and South Korea each had cases early on, but through robust use to testing, technology and social control have succeeded in preventing the explosive and exponential growth of infection represented by the “curve” we have been discussing.  Figure 5 shows daily case reports for Taiwan. Though the graph does show a curve of sorts, the peak is 27 cases on March 20th. That is in a country of 23 million people. Yesterday, the State of Massachusetts, with only a population of 7 million, had 764 new cases.

Figure 5: Daily New Cases – Taiwan

Containment works by spending a lot of time and money up front to identify cases as soon as possible, then doing labor intensive contact tracing, to inform, perhaps test, and quarantine or isolate those contacts. Done well, this can greatly reduce the effective R naught of the infection.  To introduce containment in the middle of an outbreak is even more ambitious than doing it as the start of an outbreak.  But with testing capability, enough resources, and a community supportive of the idea, it is not impossible.  If successful it can eventually reduce the total number of infections to a number managed through containment alone. It requires some individuals to submit to greater restrictions, such as when a person has been reported as a contact of an infected person, that person needs to be isolated, provided with a place to stay, provided with food and other services. But it means for the majority of citizen the possibility of loosening of social distancing, a return to work etc.  The State of Massachusetts has just announced plans to implement a containment program. The state is working the Partners in Health, a volunteer organization famous for its work against Ebola in West Africa.


The other side of the curve is unlikely to be symmetrical with the infection growth side of the curve. The other side is likely to have further ups and downs, in fact the apex that many states are anticipating in the next couple of weeks may simply be false summits on the road to greater challenges ahead. To avoid needing to maintain social distancing for months while we wait for the development of a safe and effective vaccine we may need to explore alternatives such as:

  • Effective Leveraging of Limited Herd Immunity
  • Allowing a higher rate of infection while somehow shielding the Elderly and high risk
  • Find a therapeutic treatment, and allow a higher rate of infection
  • Re-Attempt Containment

These are not mutually exclusive and aspects of all of these might be used to get the infection under better control without extending social distancing for 12 to 18 months.

Everyone stay safe!


Measles R naught

R naught for Coronavirus

Percent of population that would be infected if outbreak is unchecked

Median day on ventilators

Percentage of Massachusetts infected after current surge

Sweden response

Massachusetts Covid-19 Collabarative:

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