You’ve likely heard or read the phrase flatten the curve. But what exactly does this mean?
It doesn’t refer to flattening or squashing the virus, a curved spheroid-shaped ball into a pancake or anything like that.
Rather, the curve refers to a mathematical concept called a parabola. Infection rates usually form parabolic curves when charted, in the shape of an inverted letter U.
A parabola is symmetrical; it’s rate of ascent equal to its rate of descent.
The goal of “flattening the curve” is to create a parabola that rises and falls less sharply, when charting rate of infection, reflecting a far less extensive spread of disease over a given period of time.
A chart showing a tall parabola with practically-vertical plotting rising at a sharp angle, indicates exponential growth, or how a quantity, in the present idiom, people sick with Coronavirus, increases rapidly over a given time period.
A chart showing a parabola that has a less steep angle upwards indicates a slower increase in infection rates, as well as fewer total infections.
This function, or relation between different sets of data, is in this case the first set of data being the number of people ill with Covid-19, plotted over the second set of data, namely time.
When the rate of exchange, in this case number of people infected, with respect to a measure of time, such as number of days, is proportional to the quantity itself, we are witnessing exponential growth.
The means that if you plot the change in number of sick people on a graph, you will see a line that starts out nearly horizontal, but quickly becomes almost vertical.
This contrasts sharply with linear growth plotted on a chart with X and Y values which indicates a change of rate of something, in this case number of infections. While the chart we use is the same, with one axis being the value, time, and the other axis being the value, number of cases, the result is a straight line.
While both linear growth and exponential growth indicate a change in numerical value, the number of people falling ill with Covid-19, linear growth is a straight steady climb in number of new cases, while exponential growth is a skyrocketing of new cases.
Exponentiation, a mathematical operation, is written as two number, the second indicated as a superscript, written as though it were floating above the baseline of all the other numeric characters.
You may have seen this written as bn, or explained as base (b) and exponent (n). Alternatively, it’s referred to as base to the nth power.
Where might you have encountered this? Intermediate school, high school, or college math class. Computer programming classes.
It’s also widely used in the fields of economics, biology, and physics. In our everyday lives, this is seen in how compound interest is calculated.
To further illustrate this point, let’s say we begin with 100 diagnosed cases of Coronavirus.
Let’s say that the growth, referred to as “r” for rate of growth is 10% .That means that the rate of growth on the chart will be 0.10 per time interval, an interval usually being a day or week, depending on how we wish to chart the change in number of cases.
Each discrete interval then yields 100 × 1.102 = 100 × 1.10.
Two time intervals would yield 100 × 1.102 = 50 × 1.102 or 100 times 1.10 X 1.10.
Three of such time slices would give us 100 X 1.10 to the third power, or 100 times 1.10 times 1.10 times 1.10.
And so on. Until the curve reaches it’s peak, and then, having reach this apex, reverses at the same rate.
This results in a line on the chart that quickly grows, and now we can see where the term “exponential” growth derives from. The new value is truly an exponent of the last value plotted.
When it comes to viruses, such as Covid-19 or any other virus where people have no immunity, because it’s a new virus no one has encountered before.
The curve we refer to is the line on the chart that “goes vertical.” How can we stop this exponential growth, then?
The key lies in stopping the spread of the virus, decreasing the axis on the chart we designate as representing the number of new cases over the axis on the chart we assign for a time interval.
Exponential growth of a bacteria in a petri dish is expected; growth continues unabated until the nutrient-medium is exhausted.
But with viruses in people or animals, it’s not exactly the same. For one, the cells in our bodies are the “nutrient-medium.” The exponential growth curve relies on the virus “jumping” from one person to the next.
But, viruses do not have legs, and cannot propel themselves. So what do they do? Viruses get us to sneeze, cough, produce mucus, and spread infections viral particles in this way.
And, these methods are very effective. If they were not, influenza, Covid-19, and many other infectious viruses that spread via casual human contact would be all but gone.
Hepatitis A, B, and C are not so easy to spread. These require more intimate contact between two individuals. Therefore, we should never expect to see such illnesses growing at an exponential rate.
The best we can do is to wash our hands, avoid contact with other people, and self-isolate if we suspect that we’re ill.
Adopting measures such as limiting the number of people gathering in one place, keeping a distance between individuals, and closing businesses where people gather all accomplish the goal of halting the spread of the disease.
Social distancing, accomplished largely by avoiding public spaces and limiting people’s movement will slow down the growth of Covid-19, thereby keeping our hospitals and vital health services from becoming overburdened.
If we get sick and then recover without encountering new people, an exponential growth rate of a pathogen infecting new hosts cannot occur. Once we have recovered, we can no longer transmit the disease.
There are four basic models for how people will interact; that is, freely; quarantining only the verifiably ill; light social distancing; and heavy social distancing. Of course, there’s a continuum of new cases as we travel along this spectrum.
As can be expected, as people freely associate, a virus like Covid-19 will likewise spread freely, causing exponential growth. At the other pole, we find that acting as though each and every one of us is a carrier, more like a universal quarantine, works most effectively to stop the spread of airborne germs.
It’s imperative that we slow the spread of this virus. The United States just doesn’t have the resources to deal with rapid, unchecked growth in a population.
While it may strain us, and perhaps cause many to fall under economic hardship, it’s really the only way.
To complement this, municipal, state,and Federal governments must unburden citizens by making allowances for the sudden closure of businesses, lack of income, and general inability to earn.