Dhanada K Mishra
The late Prof Al Bartlett, a nuclear physicist and professor emeritus of University of Colorado at Boulder, once said: “The greatest shortcoming of the human race is our inability to understand the exponential function.” The coronavirus crisis provides the best case to prove his point. Bartlett was fond of proving how the exponential function is deceptive, using a wide variety of cases in which it is applicable, ranging from population growth to use of non-renewable fossil fuels.
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The simplest way to understand the exponential function is to know the difference between simple interest and compound interest. If you start with Rs 100 in the bank and the bank offers 10 per cent simple annual interest, then your money will grow to Rs 200 in 10 years. The same Rs 100 when compounded at 10 per cent interest annually would double in 7 years. If you keep doubling every 7 years, the original quantity becomes very large in few doubling cycles. Over 70 years, the same Rs 100 rupees at a compound interest of 10 per cent will yield 100 times more than at simple interest.
Another famous example from Bartlett’s lecture is of microbial growth. The doctor asks, if a pathogen contained in a bottle were to multiply by dividing itself every minute, and the container were to fill up in 60 minutes, at what time would it be half full. The answer is not at 30 minutes but at 59 minutes. It is half full or half empty only a minute to the hour. At 55 minutes into the bacterial growth process, the bottle would only be 3.125 per cent full or 96.875 per cent empty.
In the now famous 2011 movie ‘Contagion’, there is a term ‘R0’ (pronounced R nought) referred to frequently by the epidemiologists trying desperately to figure out how contagious a virus is.
This term, known as ‘Reproduction Number’, was not invented by Hollywood. It only borrowed from science. R-nought is used to describe the intensity of an infectious disease outbreak. It stands for the number of cases, on average, an infected person will pass on during the period of infection. In each previous outbreak of disease — during 2003 SARS outbreak, the 2009 H1N1 influenza pandemic and the 2014 Ebola epidemic in West Africa, the R0 estimates played an important part in characterising the epidemic and modelling its likely spread. It is something epidemiologists are racing to calculate for SARS-CoV2, the virus that causes CoVID-19.
The figure is calculated in two ways. The basic R0 is a theoretical calculation using available data to estimate the maximum number of healthy people an infected person can transmit the virus to under ideal conditions. Effective R0 represents the likely number of people to get infected given the history of vaccination, herd immunity, social distancing and quarantine measures, among other things. Therefore, effective R0 is always below basic R0. The R0 of measles, for instance, is 12-18 depending on population density and life expectancy, among other factors, whereas influenza or common flu has a relatively low R0 of between 2 and 3. Measles outbreaks are therefore often explosive, whereas flu less dramatically.
The concept of R0 was introduced by demographer Alfred in the 1920s as a measure of population growth. In the 1950s, epidemiologist George MacDonald used the same principle to estimate transmission potential of malaria. When R0 is less than or equal to 1, the epidemic is controlled.
With CoVID-19, we have seen reactions ranging from complete complacence followed by diffident and hesitant actions to outright panic. None other than President Donald Trump tweeted early into the epidemic that far larger number of people died in USA from influenza than was likely from CoVID-19. The same Trump declared an emergency and proclaimed wartime powers as the outbreak seems to have overrun the healthcare system and the economy in the most powerful country on earth.
As news of the disease being less severe on the youth became known, the younger population tended to take it much less seriously although as carriers of the virus, they were fully likely to infect someone for whom because of their advanced age or underlying health condition it could very well be fatal.
As one looks at the graphs of number of cases and the death toll, it becomes clear (Italy being the best example) that unless drastic measures of social distancing including complete and effective lockdown of entire populations are taken, the disease is likely to overwhelm a country’s healthcare system and ruin the economy. Just like the tail of an exponential curve, in each country the number of cases with time shows slow rise leading to complacence only to grow at a rapid rate soon after. While Wuhan in China, the epicentre of the disease, remedied the situation through a ruthless lockdown, Italy has been singularly unsuccessful in clamping down. The US, UK and India are a few days, if not weeks, behind Italy and we will know in the near future how successful each of these countries has been in controlling the pandemic.
For the SARS outbreak in 2003, the R0 was estimated to be 2.75, whereas for the CoVID-19, a team of scientists from Imperial College, London, has estimated a value in the range 1.5-3.5. While cases, such as Hong Kong, Singapore and South Korea, would be at the lower end of the range due to their effective action, Italy, Iran and Spain, would be at the upper end of the range.
American scholar HL Mencken believed that the nature of human species is to reject what is true but unpleasant and embrace what is obviously false but comforting. In these times of a global pandemic with grave implications, his words taken together with Bartlett’s on our understanding of the exponential function would be greatly helpful in confronting the greatest challenge to humanity since the World War II.
The writer is an academician currently visiting Hong Kong University of Science and Technology as a Research Scholar. He can be reached by email at dhanadam@gmail.com.
