COVID-19 & Epidemic Modelling

COVID-19 trumps anything we've seen in 2020.

Imagine your buddy wakes up from a 3-month coma and asks you what's happened this year.

How do you even begin? Most surely, you would start with President Trump's twitter beef with Iran, which ended with him calling in an airstrike on a general and Iran shooting down a passenger airline killing everyone. We narrowly avoided World War 3 just in time to watch Australia catch fire pretty bad. A woman tried to save the Koalas by selling pictures of her tits. Kobe Bryant died in a helicopter crash. A person in China ate a bat in a wet market and kick-started a global pandemic that infected over 2.5 million people and killed upwards of 170 thousand. All sports are canceled, all restaurants are closed, the entire world is under lockdown.

Any hope of economic growth in 2020 is gone.

Pornhub offered to help Italy build a half-decent website that can handle the millions of people applying for unemployment insurance. The US loses more than 22 million jobs in less than a month, and President Trump, in a press conference, says, "Does anyone really believe China's death toll? I've seen more body bags on television than that." Stocks fell 35 percent in a matter of weeks, and the Treasury market basically broke. Governments are spending trillions of dollars to try to support workers who lost their jobs, and their respective central banks are financing their spending, prompting memes like these. Everyone is losing their minds; half the population thinks this is the end of the world. The other half think it is all fake and are blaming it on 5G cell phone networks. Toilet paper was supposed to be the new global reserve currency but was later replaced by beard trimmers and hair dyes since no one can get a proper haircut anymore. The only thing keeping most people sane is a Netflix documentary about a homosexual gunslinging Oklahoma man with a meth addiction and 180 tigers. Oil prices are negative, and fuel will probably be used as a loss leader at gas stations by the end of the year: "Buy a bag of chips and a slurpee and get a free tank of gas!". And it's at this point you realize we're only three and a half months into the new year and 2020 already sounds like a crack head bugging out. There is enough content in the last quarter to make the previous decade seem like a bleak Swedish police drama.

Putting aside the insanity of 2020, it's clear that CoronaVirus will be a driving force in most of our lives for the foreseeable future.

There's no question that everyone has been impacted in some way by this pandemic. The hard reality is that we will likely continue to grapple with COVID-19 until a vaccine becomes available, which could take anywhere from a few months to over a year. For that reason, I think it's especially important to clear up any misunderstanding surrounding the virus and the effectiveness of specific policy responses. Without understanding what we're facing, we can't fully understand the tradeoffs that are being made by officials. With that in mind, the goal of this post is precisely that; to clear up any confusion surrounding the virus and add context to the public health response. For the latter, I am going to use a simple model developed by epidemiologists to run through some examples of epidemics. Later I'll expand on this model and make use of some extensions provided by Tim Churches, a senior fellow at Liverpool hospital in Sydney, to tailor it to the COVID-19 outbreak. As far as disclaimers go, I think it's clear that I am not an epidemiologist. I'd be hesitant to make any definitive conclusions on what's happening in specific countries from the analysis I am providing. With that said, I think the post is useful for those wondering why individual policies have been put in place over others and how effective these policies could be.

We are not dealing with the common flu.

COVID-19 spreads far more rapidly than the common flu.

It's understandable to compare COVID-19 to the flu; after all, both have similar symptoms, and both can lead to some form of pneumonia, which can make the disease fatal. Despite having overlapping symptoms, looking at COVID-19 as some version of the flu is both dangerous and wrong. Several key differences make COVID-19 far more deadly than the common flu. For starters, let's look at the incubation period, which is the time it takes for someone with the virus to start showing symptoms. The flu's incubation period ranges from 1-3 days, far shorter than COVID-19's, which can be anywhere from 5-14 days (or more). For COVID-19, the kicker is that scientists believe that you could be contagious throughout this entire incubation period. That's unlike the flu, where you become contagious once you develop symptoms. Of course, that facilitates the spread of the virus.

COVID-19 is a novel virus.

I think this point is very under-appreciated. We have not seen this particular type of CoronaVirus, and scientists are learning about this virus as things unfold. Since the virus is novel, no one has had it before, and nearly everyone is susceptible to getting it. That's in contrast to the common flu, which, apart from certain people having natural immunity to it every year, there is also a flu shot available to help stop the spread. The fact that almost everyone can get the virus is an important distinction as we could easily overwhelm the healthcare system.

Healthcare systems are being overwhelmed.

Without controlling a very contagious virus, healthcare systems could quickly become overwhelmed. In the early stages of the epidemic in China, many thought that the relatively low mortality rate of COVID-19 at around 4 percent (which is frankly not that low) wouldn't impact the overall economy. The notion that people would learn to "live with it" touches on "herd immunity," the idea that you need the population to build up a tolerance to the virus. That would have been an "acceptable" approach were it not for COVID-19's alarmingly high hospitalization rate of 15-20 percent. These severe complications are putting a strain on healthcare systems and place healthcare practitioners in a situation where they must choose which patients to treat and which to send home. Of course, this is problematic because patients are unable to receive proper care and end up dying. Furthermore, the lack of personal protective equipment (PPE) for frontline healthcare works means that these workers are also getting the virus and, in some cases, dying.

Herd immunity is unfeasible.

With the healthcare system overwhelmed, the death rate of the virus will undoubtedly increase. The chart below shows the death rates of countries across time. Although this chart is biased in many ways (it does not control for age and pre-existing health conditions), the point is that, as the death rate increases, people are not going to be "okay" with getting the virus. You could send people back to work, and, in theory, they will produce something, but who will buy it if everyone is afraid of getting the virus? Expectations about the future are a big part of consumption and production. Despite politicians appealing to those who have lost their jobs, people simply won't spend as they used to until healthcare experts can assure people's safety. That leaves the idea of herd immunity dead in the water.

The alternative is to "flatten the curve."

The message is simple, preventative measures, such as social distancing and hand-washing, help take the strain off of the healthcare system by reducing the number of people that are infected at any given point in time. Infographics (like the one below) help convey the message that stretching out the length of the virus will help ensure that those who need medical help will actually get it. Although I support the message, these types of illustrations have several short-comings. For starters, they assume that epidemic curves are both symmetric and equal in density. In reality, curves may not be symmetric, especially when you consider policy changes after the peak in cases. An example of that would be "liberating" American states after daily new cases start to decline. These new policies may result in a "2nd wave" of infections, which could have an even higher peak and a thicker right tail of the distribution. On the density side, the assumption that the number of people who get the virus is constant is not correct. Although the premise that we save lives by spreading out cases is correct, we also save lives by lowering the basic reproduction number of the virus (i.e., we reduce the overall number of people who are infected).

Source: https://thespinoff.co.nz/society/09-03-2020/the-three-phases-of-covid-19-and-how-we-can-make-it-manageable/

The ultimate goal of all policies is to reduce R-nought.

Scientists measure how contagious a virus is through the R0 (R-nought). R0 can be thought of as the number of people each person with the virus infects. For the common flu, the R0 is around 1.3, while COVID-19's is between 2-2.5. The higher R0 helps explain the rapid rise in cases over the last month and the reason why we've seen such a robust public health response to the pandemic. The ultimate goal is to reduce the R0 to at least one if not lower. Once that happens, the virus is then stable or dying out. One of the most effective ways to do this is through vaccination as it provides your body with antibodies to fight off the virus, removing you from the pool of people susceptible to the infection.

Mitigation and containment are the best policy tools for a novel virus.

The workhorse of epidemic modelling is the SIR model.

A commonly used framework for modelling epidemics is the SIR (Susceptible, Infectious, Recovered) model. The model breaks the population up into the three groups above and then estimates the rate at which each member transitions between the groups. The model simulates individual members of the population and allows them to interact with each other with some probability of getting the virus at each interaction. With this type of model, we can explore different public health interventions and gauge their effectiveness. For instance, we can estimate the effect of hygiene measures, such as hand washing, wearing a mask, and avoiding face touching, by reducing the probability of infection at each interaction. For social distancing, we can reduce the number of interactions people within the model are allowed to have each day. The flow chart below shows how agents in the model transfer between different states.

Source: https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

The R0 of the virus is a function of social distancing and personal hygiene.

The chart below shows the output of the SIR model using several combinations of social distancing and hygiene measures. On each chart, the X-axis represents the time since the first case. Meanwhile, the Y-axis measures the percentage of the population in each group. Each row represents varying degrees of hand-washing, and each column outlines different levels of social distancing. The bottom right corner assumes no social distancing or hand-washing, while the top left shows maximum social distancing and hand-washing. Something that will probably catch most people by surprise is how quickly the virus can spread. With no policy response, we see that the entire population is infected within 20 days. We can see that both policies have a fairly substantial impact on the spread of the virus, and, unsurprisingly, a combination of the two is the most effective. We can see that the virus is stable with maximum social distancing and hygiene measures and that the R0 is a function of these preventative measures.

Policy changes have an impact on the R0.

What would happen if we decided to go from maximum social distancing and hand washing to a less extreme policy? The chart below carries the same format as the one above; however, at time 100, varying degrees of social distancing and hand-washing are relaxed. For the initial 100-days, we use the case where we continue to have maximum social distancing and hand-washing (the top left corner). Once these aggressive policies are relaxed, the R0 starts to increase, and the virus continues to spread as it did in the first scenario. That's a depressing conclusion. The model suggests that sacrificing so much in the short run has little impact on the final result. On its own, that's not that surprising. The whole point of these preventative measures is to buy time for scientists and doctors to come up with permanent solutions, like a vaccine. These permanent solutions aren't included in the base model and, therefore, the conclusions we draw from this aren't necessarily accurate. With that said, they help motivate why permanent solutions, like vaccines, are needed.

Increased testing capabilities will allow parts of the economy to open.

Why is testing necessary?

The economic hardship of social distancing has been widespread, and, as I suggested above, these types of policies are unsustainable for long periods. With a vaccine likely more than a year away, an alternative solution is to increase testing capacity. By identifying who has the virus, we can stop those individuals from spreading the virus by quarantining them. This type of information becomes invaluable to policymakers, as they can reopen the economy in stages (county by county, etc.). To better understand these dynamics, we, unfortunately, need a more complicated model. The flow chart below shows a more representative model of COVID-19 that Tim Churches has developed. In the original model, we had three states: susceptible, Infected, and recovered. Tim's model introduces a few more. People in the model can now be infected and asymptomatic, infected and symptomatic, quarantined, hospitalized, recovered, and they can die.

Source: https://rviews.rstudio.com/2020/03/19/simulating-covid-19-interventions-with-r/

Social distancing and testing both reduce the spread of COVID-19.

The graph below shows the output of the new model. We can see that the base case's R0 is much lower in the model we introduced above. That is due to the new states in the model, where people can quarantine and be hospitalized etc. Under the base case, almost the entire population gets infected within the first 50 days of the outbreak. When we introduce social distancing policies, we can see that the virus spreads much more slowly. In this case, we implemented a gradual increase in social distancing after day 15 up until day 30, where people go from seeing ten people a day down to five people. The policy works in that it reduces the R0; however, we still have nearly 75 percent of the population infected within the first 50 days. The panel on the right shows what would happen if we just increased testing without social distancing. In this example, we gradually increase testing from 2 percent of people that are symptomatic to 50 percent of people showing symptoms. Right away, we can see that this policy is more effective than social distancing. That makes sense; after all, we are identifying people who are sick and quarantining them from others. This type of policy gets to the heart of the issue because it stops people who are infected from infecting others. Like before, a combination of the two strategies provides the best results.

If we decrease social distancing without proper testing, we will guarantee a second wave.

I mentioned that assuming that case curves are symmetric may not be realistic if policies change. Implicitly, I am assuming that we get a second wave unless these permanent solutions (vaccines and testing) are in place to help stop the spread. In the example below, I show what could happen if we do not increase testing but decide to reduce social distancing (this is akin to reopening the economy). The base case is on the far right and shows what would happen if we aggressively increased social distancing from day five to day ten and continued to social distance up until day 30 (The black line). From day 30 onward, we gradually decrease social distancing. We can see that under the base case, the case count increases once we stop social distancing, and nearly everyone ends up getting the virus. If, however, we combine social distancing with increased testing capabilities, we can see that we can contain the spread of the infection. In this example, I assume that testing gradually increases from day 15 to day 30, from 2 percent of symptomatic individuals to 50 percent and 75 percent, respectively. The bottom line here is that to reduce social distancing measures, we need to increase testing capacity. Without that extra capacity, we will just experience a second wave of infections, and all of the hard work that was put towards containing the virus will be for nothing.

These are just models.

Like I had mentioned above, the goal of this post was to provide some nice looking visuals to help add context to the recent public health responses. Model-based approaches like these are useful to simplify the problem and tinker with it, but the reality is, the world is complicated. Presumably, COVID-19 won't behave as well as it has in these simulations that I've run but, the hope is that at least I've captured the gist of what policymakers are thinking.

Thanks for reading and stay safe.

Tiago Figueiredo