Question

16) The COVID-19 Outbreak has put the world on pause as we discuss the best way to "Flatten the Curve." In 200 words or more, explain what it mathematically means to "Flatten the Curve" from a BioCalculus perspective, and why it matters. Include in your explanation each of the following topics: • • • • • • The SIR Model, SEIR model, or other variant of the Kermack-McKendrick model. Ordinary Differential Equations. Partial Derivatives and/or Partial Differential Equations. Limits & Long-Term Behavior. Exponential & Logistic Growth. Integration, the Fundamental Theorem of Calculus, and/or Riemann Sums. Your explanation should be written as though you are explaining it to a D-range Calculus I student who doesn't understand why they need to learn Calculus, doesn't understand why the college is closed, and doesn't wash their hands after they go to the bathroom (gross).

Answer 1

People travelling into Australia will now have to self-isolate for 14 days – one of a range of measures announced at the weekend by Prime Minister Scott Morrison, with the aim of slowing the spread of the coronavirus and easing the stress on hospital beds.This general concept of slowing the virus’s spread has been termed “flattening the curve” by epidemiologists – experts who study how often diseases occur in different populations, and why. The term has become widespread on social media as the public is encouraged to practise “social distancing”.

Exponential growth-In the early stages of an epidemic, when most people are susceptible to infection, mathematicians can model a disease’s spread from person to person as essentially a random “branching process”.If one infected person infects two others on average, the number of infected people doubles each generation. This compounding is known as exponential growth.Of course, an infected person is not going to infect others. There are many factors affecting the likelihood of infection. In a pandemic, the growth rate depends on the average number of people one person can infect, and the time it takes for those people to become infectious themselves.

Flatten the curve

Health authorities around the world have been unable to completely prevent COVID-19’s spread. If cases double every six days, then hospitals, and intensive care units (ICUs) in particular, will be quickly overwhelmed, leaving patients without the necessary care.But the growth rate can be slowed by reducing the average number of cases that a single case gives rise to.In doing so, the same number of people will probably be infected, and the epidemic will last longer, but the number of severe cases will be spread out. This means that if you plot a graph of the number of cases over time, the rising and falling curve is longer but its peak is lower. By “flattening the curve” in this way, ICUs will be less likely to run out of capacity.

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Flattening the curve is another way of saying slowing the spread. The epidemic is lengthened, but we reduce the number of severe cases, causing less burden on public health systems. The Conversation/CC BY ND

As there is currently no vaccine or specific drug for COVID-19, the only ways we can reduce transmission is through good hygiene, isolating suspected cases, and by social distancing measures such as cancelling large events and closing schools.