https://www.wsj.com/articles/when-a-virus-spreads-exponentially-11585850494
The key to stopping the Covid-19 pandemic lies in lowering the rate at which infections multiply.
Fighting a pandemic like Covid-19 requires experts in many fields: epidemiologists who study the spread of disease, doctors who treat the sick, scientists who work on finding a vaccine. There is math involved in all of these specialties, but math can also help us to make sense of the barrage of information that we’re receiving daily.
The starting point is the math of exponential growth. The word “exponential” is sometimes used informally to mean “really fast,” but mathematically it means something very specific: that a quantity is repeatedly multiplied by the same number. When a virus spreads, each infected person goes on to infect a certain number of other people, on average; this is called the reproduction number or R0. Then each newly infected person goes on to infect R0 people, again on average.
Exponential growth is dangerous, because if each person infects more than one other person, the spread of disease quickly becomes overwhelming. Multiplying by 3, for instance, it only takes 21 steps to reach 10 billion, more than the current population of the world. We start with very low numbers that seem insignificant, but it’s not the absolute numbers that matter, it’s the rate at which they’re increasing, which also increases exponentially. Waiting until an infectious disease feels like a problem is too late to start addressing it.
One important feature of exponential growth is that it’s not helpful to look at the number of new cases each day. Exponentials increase by multiplication, so it’s more relevant to look at the percentage increase each day. This is what “flattening the curve” is about: reducing the rate of multiplication. Eventually we need the rate to be less than one, so that each infected person infects fewer than one new person, producing exponential decay instead of growth.
No comments:
Post a Comment