COVID-19 Modeling

With the current COVID-19 pandemic rapidly spreading through the world, two highly-talented FIT students, Ritisha Sharma and Jasrayman Thind, and I have decided to provide some simple epidemiological models for projecting the spread of the disease through some countries.

Our work is ongoing, more broadly focused on modeling different diseases, and is in its early stages, but some preliminary results using only slightly modified standard models are available. The quality of models depends highly on the quality of the data, which varies from country to country, but the models do seem to capture some of the main dynamics of the spread of the disease.

We have chosen to use standard SIR models with time-dependent parameters. These models break the population into three groups: Susceptible people, Infectious people, and Recovered people.

  • The Susceptible group contains people who have not contracted the disease.
     

  • The Infectious group contains people who have contracted the disease and are contagious.
     

  • The Recovered group contains people who have contracted the disease but have recovered or died.

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The contact rate, which measures how contagious the disease is and how much infectious and susceptible people come into contact with one another, and recovery rate, which is the percentage of infectious people who recover (or die) per day, are each allowed to change at one day, optimized to fit the data,

[JUNE 6: THE INFORMATION BELOW IS OUTDATED, POLICY CHANGES SEEM TO HAVE CONTRIBUTED TO A NEW SURGE IN CASES, AND STRICT LOCKDOWNS WERE RE-INSTITUTED.]

Projections for the Kingdom of Jordan are available below.

The plot begins on March 11, when Jordan had just 1 known case of the coronavirus and continues through July 21. The solid lines are projections and the dots are the real data showing how many people were in each group each day.

Be careful to notice the scales on the two vertical axes.

 

  • Susceptible is measured on the left axis, which has much larger numbers since a very small percentage of Jordanians have contracted the disease and the model suggests not too many will contract it.
     

  • The infectious and recovered groups correspond to the scale at the right, only measured in the hundreds.

As you can see, the model fits the data quite well. Overfitting can be a concern given the relatively small set of data, but the model has just 6 parameters. It seems the growth in infectious cases was measurably reduced in late March.

Check back for more results, more of the math behind our work, our code, and a web app soon!

References

[1] 2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository by Johns Hopkins CSSE (https://github.com/CSSEGISandData/COVID-19)

[2] World Bank (2020). World Development Indicators, National Population Table.

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