Many models for the expected impact and spread of the virus are being shared on social media and reported in popular news. Below, we hope to point you to a couple of such models and provide a basic introduction to the assumptions that they use and their key conclusions about what we can do to slow the spread of the virus.
Almost everyone in a population is susceptible to be ill because our immune systems have not recognized an organism like this before.
Current estimates for R0 vary, considered to be somewhere between 2-4. This means each infected person will transmit the virus to 2-4 other people during the course of their illness. Most models assume a value of around 2.3 (Tuite et al. 2.5.20), which is higher than the estimated R0 for the seasonal flu (~1-2) (Callaway et al. 3.18.20).
We can quantify how quickly a virus spreads by the virus doubling time (the time it takes for the number of cases to double). In the early days of the pandemic, the doubling time was estimated to be 5-7 days for the U.S. (Lin, M. Lin Lab Presentation 3.13.20); the estimate as of 9.7.20 is 2 months for the U.S., though it varies by state.
We are assuming patients cannot be re-infected with the virus in the short-term (months-years). As discussed in Module 1, this is an open question, and will only be answered with data gathered over the coming weeks or months. It is important to note that some apparent reinfections reported in case studies may reflect deficiencies in test specificity. Apparent reinfections in South Korea, for example, were later confirmed to be false positives
Creating a complete, accurate model for the spread of SARS-CoV-2 will require the expertise of multiple highly trained scientists and complex computational tools. We will not present such a model here. Instead, we hope to introduce an intuitive, simple model that helps explain the spread of the virus based on current data. Such a model is being used to make estimates about how many people will get sick from SARS-CoV-2.
This video describes what we can expect from the simplest model of virus spread, using real data. If there is only one thing that you click on in this section, it should be this video. It’s only 9 minutes long (4.5 if you watch at 2X speed). We will emphasize some key take-aways from the video below:
CORE VIDEO: Exponential Growth and Epidemics
The epidemic spread is modeled by an exponential curve at the beginning, because most people have not been infected by the virus yet and are therefore susceptible to infection. This is what the spread of the virus looks like right now based on existing data; the scale on the y-axis is a log scale, so cases grow a lot quicker as time goes on in the x axis. (Note: a limitation of an exponential growth model is that it assumes homogeneous mixing of individuals in the population, which is not true, especially in the latter stages of an epidemic).
As more people are infected, the spread of an epidemic slows down because there are fewer people who can still get sick from the virus. The spread of virus will eventually slow down and look logistic:
Without a vaccine, the majority of people in the entire world will eventually become infected by SARS-CoV-2. This is why the logistic curve flattens out: because there will be no one left to infect. Our goal is for the spread of the virus to slow down, so that our healthcare system can provide the best possible clinical care for the critical cases of SARS-CoV-2 coming in every day, along with the routine clinical cases that you would expect irrespective of the pandemic (heart attacks, cancer treatments, hip replacements, car accidents).
In the worst case scenario, if we do nothing to change the disease doubling rate, the CDC estimates up to 214 million cumulative infections (⅔ of the American population), and 1.7 million deaths (assuming 1-2% case fatality rate) in the United States in the coming months (NYTimes 3.13.20).
Our main strategy to stop these outcomes is mitigation: we cannot stop transmission completely, but we can reduce the pandemic’s impact on the healthcare system.
CORE TEXT (simple model to illustrate concept): Stevens, H. Why outbreaks like coronavirus spread exponentially, and how to “flatten the curve.” Washington Post, March 14th, 2020.
Supplementary material: a tunable model that allows the user to change model parameters to visualize how they could affect virus spread.
There is a lot to be hopeful for. Regions that implement these mitigating interventions, which use social distancing to slow down and reduce the spread of the virus, may reduce the Re. If we can reduce the Re by half (from 2-3 new cases per infected person to ~1.2 per case), then the doubling time will be 4 times longer. Indeed, we are already seeing these effects in the U.S. Siedner et al. (medRxiv, 4.8.2020) calculated the daily epidemic growth rate by confirmed cases in all 50 U.S. states, before and after each state implemented its first mandatory social distancing measure in mid-late March. On the 4th day after implementation -- consistent with viral incubation period -- the mean daily COVID-19 growth rate dropped 0.8%, which corresponds to an increase of average doubling time from 3.3 days to 5 days nationwide.
The key take-away is that social distancing measures will have a profound effect in delaying the “peak” in the number of critical COVID-19 cases in the US. We buy the healthcare system valuable time to get ready for this crisis by increasing the personal protective equipment, beds, ventilators, and healthcare workers available to care for those critically ill from the virus and from causes other than the virus, decreasing overall mortality. This is why social distancing is critical.
Simulations show that slowing disease spread by a couple of months will dramatically affect the number of critically ill COVID-19 patients who can get hospital beds:
In the figure above, each line describes the number of simulated COVID-19 cases under different assumptions about the total number of infected cases needed to establish herd immunity (20, 40, or 60%) and the success of social distancing. Successful social distancing is simulated, "flattening the curve," such that the spread of the virus lasts 6, 12, or 18 months respectively. Full simulation linked here.
Actually implementing social distancing requires fundamentally changing our habits and daily routines. Though all 50 states have adopted some form of social distancing measure as of March 27th, adherence varies city to city and even household to household. The brief article below makes these recommendations concrete and clear, including reducing all public gatherings of any size, ceasing visits to others’ homes, and limiting trips. We recommend reading it if you haven’t already, and sharing it with friends and family.
CORE TEXT: Bitton, A. Social Distancing: This Is Not a Snow Day, Ariadne Labs, 3.13.20