Exponential Growth explained for the COVID-19 (Coronavirus) Epidemic

Oxford University Mathematician Dr Tom Crawford explains exponential growth in the context of an epidemic such as that for COVID-19/Coronavirus. Beginning with one primary infection we see how the number of cases increases dramatically over a period of only 30 days to more than one thousand. All sources are referenced below.

The value of the reproductive number R0 = 3 is taken from current World Health Organisation estimates. Please see here for more information.

The data for the UK population is from 2018 and is sourced from Statista here.

The data for the COVID-19/Coronavirus death rate is from the Chinese Centre for Disease Control and Prevention. Please see here for more information.

Oxford Mathematician explains SIR disease model for COVID-19 (Coronavirus)

The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population. I first explain where the model comes from, including the assumptions that are made and how the equations are derived, before going on to use the results of the model to answer three important questions:

  1. Will the disease spread?
  2. What is the maximum number of people that will have the disease at one time?
  3. How many people will catch the disease in total?

The answers to these questions are discussed in the context of the current COVID-19 (Coronavirus) outbreak. The model tells us that to reduce the impact of the disease we need to lower the ‘contact ratio’ as much as possible – which is exactly what the current social distancing measures are designed to do.

Produced by Dr Tom Crawford at the University of Oxford.

How are humans affecting bird populations in the UK?

Over the past 60 years since bird feeders first became commercially available, humans have been changing bird populations across the UK. The overall effect has generally been positive, with an increase in the prevalence of Wood Pigeons, and a shift in the migration pattern of Eurasian Blackcaps, but as with most changes, there is a word of warning… Live interview with BBC Radio Oxford.

How long is a lightning bolt?

A new record flash stretching all the way from Texas to Kansas was discovered recently in data from the GOES-16 spacecraft, though the record may soon be broken… Live interview with BBC Radio Oxford.

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