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Modelling a Pandemic

                             

We learn from history that the Black Death took about five years to spread to Europe from China. It took the coronavirus SARS-CoV-2 only about five weeks to do the same. Planes, trains, and mass transit: we definitely live in a much more globally connected world now.

In December 2019, very little was known about a mysterious pneumonia-like disease reported in Wuhan, China. And yet, by March 11, 2020, the World Health Organization (WHO) declared a pandemic after the disease, now called COVID-19 was found in 110 countries worldwide. We as individuals have questions: what is happening, what is our risk of dying, and are our friends and relatives going to be safe. Governments want to make the right policy choices: they need to know how many people might die, how many will be hospitalized, and when to direct and later lift a lockdown. These policy decisions require us to understand the basic science and economics to do our own risk management until the pandemic is over.

There is such a current distrust in science that rumours and conspiracy theories are rampant. As Tim Caulfield tweeted sarcastically, “Elvis and Tupac created #COVID19 on the Grassy Knoll using #Area51 #5G technology!” This statement didn’t even include Bill Gates, Dr. Fauci and big pharma.

As teachers, we can assist our students in recognizing the difficulty of the political decisions by scrutinizing a simple mathematical model of a pandemic. We need to help our students understand that we are all in danger of omitting evidence-based decisions in favour of immediate emotional reactions, especially to the daily onslaught of pandemic news.

In previous blog posts, I have described the skills of a scientist as outlined in the Alberta science curriculum:
   •observing
   •classifying
   •measuring
   •inferring
   •predicting
   •interpreting data
   •controlling variables
   •making operational definitions
   •making hypotheses
   •experimenting

Many of these are key skills in the making of a model for pandemics. To help us understand how complex modelling works, let’s look at a simplified SIR Model. The name comes from the formula P=S+I+R. Here we use our operational definitions. The population (P) is made up of three types of individuals: susceptible (S), infected (I) and recovered (R).
We can consider the model with a minimum of mathematical knowledge and we can see the derivation of the curve invoked in the phrase ‘flatten the curve’.

In the illustration below, the Population is shown on the vertical (Y) axis and Time on the horizontal (X) axis. The simplified SIR model requires a lot of unrealistic assumptions. For example, at the beginning of an outbreak, 100% of the population is susceptible. The susceptible then become infected at a constant rate. Over time, the number of infected increases. Then, as the infected recover, the number of infected reaches a peak and begins to decrease. The total S + I + R always equals 100%. In this model, there is no defined death rate.

                              

I have provided a link below to an interactive SIR Model provided by the Complex Systems Digital Campus. You can manipulate the initial population, the infection rate, the number of initial infected and the effect of a vaccination to see the effect on the curve.

Science advisors are using much more complex mathematical modelling than the SIR model with many more variables to advise politicians. Politicians may say they are following the science, but realistically, they must also address the emotional and economic needs of their citizens. Some of the early predictions seem to be wildly wrong, but the model only predicted a range of possible outcomes. Yet, seeing these early predictions changed people’s behaviours in such a way that the variables all changed. I heard the following example. If while driving, we all ran red lights, the predicted death toll could be quite high. Most of us realize the danger and therefore obey the traffic signals – not because it is the law, but for our own self preservation. Similarly, when the infection rate of the SARS-CoV-2 seemed high, most of us were willing to follow the ‘social distancing’ and ‘stay at home’ protocols. The simple SIR Model won’t help us predict the future, but it will help us and our students understand the changing public policy with regard to COVID-19.

You can learn more about COVID-19 by following the link below to additional posts on our Genome Alberta blogs.

Some of my ideas and opinions expressed in this post have been shaped through the course COVID-19: Pandemics, Modelling, and Policy offered by: UNESCO UNITWIN Complex Systems Digital Campus through Future Learn.

Links of Interest:
   Interactive SIR Model
   Science Lessons from COVID-19
   COVID on Genome Alberta
   Gerry Ward on Twitter @GWardis

Modelling a Pandemic

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