The Mathematics Behind the Covid-19 Outbreak

What is Covid-19?

According to the World Health Organisation (WHO), Covid-19 is ‘novel’ because it has not been identified in humans before. Because of this, humans are likely to have low, or no, prior immunity to the virus. It causes respiratory illness with symptoms that include runny nose, sore throat, cough, and fever. It can be more severe for some persons and can lead to pneumonia or breathing difficulties. 

As of 11th February 2020, 25 countries had a total of 43,107 confirmed cases of the coronavirus and there have been 1,018 deaths.

The Spread of Covid-19 

The two key factors that determine how quickly a disease will spread are:

1. The average number of people a single person is likely to infect

2. How long it takes for these infections to happen

R0 (pronounced as ‘R naught’) is a mathematical term that indicates how contagious an infectious disease is. R0 tells the average number of people who will catch a disease from one contagious person. It is specifically applied to a population of people who were previously free of infection and haven’t been vaccinated. 

Several teams around the world have used models to estimate R0 from available case data. Depending upon the methods used, estimates of R0 for the new coronavirus have ranged from 1.3 (similar to seasonal influenza) up to 3 or 4 (similar to SARS). 

Professor James McCaw of University of Melbourne is part of a working group convened by the WHO to attempt to model the spread of the virus in the general population. The group’s modelling shows that each infected person tends to infect three other people. That makes it more infectious than the flu, but less infectious than SARS and much less infectious than measles, where one person is like to infect up to 20 people. 

Source: Professor James McCaw

The ‘serial interval’ is related to how quickly a virus multiplies, and it can have a big effect on the model. Early estimates indicate that the new coronavirus has a serial interval of around 7 days, which is substantially longer than for influenza which sits at around 3 or 4 days. 

While it may seem that a more severe disease would be of greater concern, it may be easier to control. When symptoms are severe, infected people are more visible, making them easier to identify, quarantine and treat. In fact, people experiencing severe symptoms are more likely to reduce their contact with others, so reducing the rate at which they spread infection.

Besides that, China introduced travel restrictions on 23rd January 2020 which affected 20 million people, later extending these to around 50 million people. These restrictions may have come too late to prevent the spread of outbreak to other parts of China, but there is still hope that they may help limit global transmission. However, models of past outbreaks suggest that while travel restrictions may delay the spread of an outbreak, they have less effect on reducing its size. 

Conclusion

As new information emerges during an outbreak the assumptions and data that feed into models are updated, leading to a constant revision of estimated risks, impact and controllability. There will always be uncertainties both in the data captured during an outbreak and the estimates generated by models. 

This post was originally written for the Heriot-Watt University Students’ Actuarial Society March 2020 Edition.

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