Imagine a world in which the only way to get a soda is to get your doctor to write a prescription. It costs $20 per can. Your insurance company pays. The economy produces about 100,000 sodas each day.

If you lived in this world, do you think you could get people to scale up the production of soda to a level of millions of cans per day? It would be a challenge, but not because it is hard to produce and distribute soda.

America is confronting two crises: an economic crisis laying waste to our livelihoods and a health crisis threatening our lives. The twin crises are deeply intertwined: our economy cannot be reopened without credibly addressing fears of infection and resurgence.

How much difference does it make if the test used to send people into quarantine is bad? Not as much as you might think.

The simulated data here contrast policies that isolate people who test positive using four different assumptions about the quality of the test. Even a very bad test cuts the fraction of the population who are ultimately infected almost in half. And when I say bad, I mean bad – an 80% false negative rate, which means that 4 out of 5 of people who are truly infectious will get a negative test result – i.e. a result saying that they are not infectious.

In a previous post, I presented a “dots in a box” model of the spread of a virus. In this post, I use it to compare the economic and social cost of two policies that are equally effective at containing the virus.

What the simulations show is that if we use a test to determine who gets put into isolation the fraction of the population that needs to be confined and isolated is dramatically smaller. These benefits are available even with an imperfect test and without doing any contact tracing. It does take frequent testing, with each person getting retested roughly every two weeks.

To understand the effects that more testing could have on the course of the pandemic, I constructed a simple model that I could use to simulate and visualize the effects of different policies. This post, the first in a series, introduces the model. In a follow-up post, I’ll use the model to compare the effects of a policy of nonspecific or uniform social distancing with those from a targeted policy that uses tests to make sure that someone who is infectious is more likely to be quarantined.

This is not the type of model one can use to capture the actual course of the disease. For that purpose, only a fully fledged model of the type developed by epidemiologists will suffice. Instead, it is a toy model that allows a visualization that helps explain how the more complicated models work. That said, it also has enough structure to offer some insight into two relevant questions that we should be asking:

1. How much difference does it make to the outcome if the test used to decide who gets isolated has a higher false negative rate. Answer? Very little.

2. If we contrast a nonspecific policy of social distance with a targeted policy guided by frequent testing that is equally effective at containing the virus, how much more disruptive is the nonspecific policy? Answer? Way more disruptive.