Coronavirus Latest: The maths behind contagions

The way scientists calculate risk and the way the rest of us do, is similar but different! Scientists use a lot of statistics and mathematical modelling, and the rest of us may do some maths, but we also throw in common sense notions, and advice that has been bandied around from all quarters especially from where we get our news. We are all distilling what we know about coronavirus to determine whether we are at risk and what we should do. That is why there is always a constant need for clear and unambiguous official public health advice.

There is a lot of maths associated with predicting the spread of a new infectious disease. How many days are people contagious once they are infected with the virus? How often is an infected person likely to be in contact with other people each day? What is the likelihood of infecting those they are in contact with? There are environmental factors to take into account as well as the age and health levels of those infected.

Ro is the basic reproduction number of an infectious disease which represents the average number of people who may catch the virus from an infected person, in a population where no one is immune to the disease. The reproduction number for the new coronavirus: SARS CoV2 is estimated as between 1.4 – 2.5 by the World Health Organisation, although other estimates are higher, over 3.2. Ro calculations can vary from country to country.

Scientists can forecast how serious an outbreak may become by using this calculation. But Ro just measures contagion, rather than how deadly the virus may be. For some diseases like measles the Ro is very high, as high as 18 people infected. For diseases such as Ebola, the Ro is far lower (estimated at around 1.5, although there is a range between 1.5 – 2.5 between different countries). These figures help to identify the number of people who may need to be vaccinated in order for the population to reach “herd immunity”. This phrase means that if a high enough proportion of people in a population are immune, it is less likely for the virus to find and infect the few susceptible people. If the Ro number is high, then a higher number need to be vaccinated.

There are other calculations to determine how effective a vaccine is. A vaccine for the new coronavirus is being developed but likely to be some months away before it is fully tested and available.

Meanwhile, with a new infectious disease, at the beginning there is a mismatch between what the scientists are trying to find out (what is the genetic profile of this virus, what is the incubation period of the virus, how do we develop the vaccine quickly enough etc etc), and what the public need to know (ie, what do we do, and can we go about our daily business, go to school, go to work, use public transport etc).

Public Health England is the national body which shares the health advice with all local authorities and NHS bodies. The international, national and local media are ably filling any gaps, by sharing public health advice.

When in doubt, I think a flowchart is always a good idea! It separates the wheat from the chaff and spells out the wheat! (Even if there have been recent criticisms of the advice being delayed or all chaff!) I reproduce here the advice on managing a suspected case of the novel coronavirus (aka SARS CoV2, aka 2019-nCov, aka Covid19).