On Monday, March 15, the US had about 4, confirmed cases. So then you might think the total will grow by 4, every two days. It's much worse than that. What you need to look at is the percentage increase. In this case, it doubled an increase of percent in two days. At that rate, it will grow from 8, on Wednesday to 16, on Friday, and 32, by Sunday. Maybe this popular parable will give you a feel for exponential growth: A kid wants to boost her allowance, and she proposes an unusual deal.
Her parents would pay her daily, but the amount is only 1 cent today. Then it increases: 2 cents the next day, 4 cents the next—you get the idea.
Small change, right? So how do you model the spread of a viral infection? And why is it called exponential growth anyway? Let's start with some basics. Suppose we have a population, and a certain number N of them are carrying the Covid virus. When N is 1,, there will be new cases the next day. When N is 10,, there will be 2, new cases the next day.
But here's the crazy part: This is like a car that is moving, but the speed depends on where it is. The farther it goes, the faster it goes. In this analogy, the distance traveled is like the number of people infected. You can obtain a formula for N as a function of time analytically using differential equations , but let's solve it numerically first.
Oh, a numerical calculation is where you break the problem into small time steps. At each step, I will calculate the number of infected people and from that calculate the number for the next day. Using the rate of change formula above, I get the following infected update expression:. That makes sense, right? The rest is fairly straightforward.
It's so simple even a computer can do it. I like that joke. View Iframe URL. Coronavirus was declared a global pandemic by the World Health Organization, but what does that mean and how is a pandemic different from an epidemic? What is an epidemic? Examples of past epidemics are the: Spanish flu measles outbreak from to whopping cough What is a pandemic?
In short, a pandemic is an epidemic on a national or global level. Why declare a pandemic? Coronavirus in Our Community Stay up-to-date on the spread of COVID with information on symptoms, prevention, vaccine updates, testing, and how you can help. Read the Latest. Find a Location Near You. Women's Health. Updates: Coronavirus in Our Region Read the latest numbers on coronavirus cases in the Finger Lakes and Greater Rochester, as well as local regulations and travel restrictions news.
View Cart. Join Now. NCTM Store. Toggle navigation MENU. Log In Not a member? Pandemics: How Are Viruses Spread? Grade: The spread of a virus is influenced by four factors.
Instructions This math simulation models the spread of a virus through social contact. Exploration How Are Viruses Spread? Here are four factors: the size of the population of opportunity; the number of days contagious; the number of people with whom an infected person comes in contact; and, the probability of contracting the virus from contact with an infected person. What is a Pandemic?
According to the World Health Organization WHO , a pandemic can start when three conditions have been met: a new virus subtype emerges; it infects humans and causes serious illness; and, it spreads easily and sustainably among humans.
The History of Pandemics An epidemic is an abnormally high occurrence of a disease in a particular population or geographic area. How to Minimize the Threat of Pandemic Even as early as , officials knew that contact with infected persons caused the virus to spread.
How would quarantine affect the spread? Which parameter population, days contagious, number of contacts, or chance of contraction does it change in the applet?
Hold the other variables constant and change only this variable in the applet. What happens? A medicine is developed that reduces how long infected people are contagious. How would this affect the spread?
Which parameter does this medicine influence? A medicine is developed for uninfected people to take that will decrease their likelihood of contracting the disease. Which parameter does this medicine affect in the applet? Try using the applet again, holding two variables constant. Disease and History, 2nd revised edition. Nobilon International. World Health Organization. Half of the people are accounted for below the point of inflection, and half are accounted for above the point of inflection.
Half of the time is accounted for to the left of the point of inflection, and half of the time is accounted for to the right of the point of inflection. Once the point of inflection is known, it is possible to estimate: How long a pandemic will last. Since half the time occurs to either side of the point of inflection, the point of inflection is the midpoint of the curve.
Therefore, if a pandemic has lasted x days in getting to the point of inflection, it will likely continue for another x days.
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