R0 value, lotus leaf and Covid-19

By Dr. Sumedha S. Amarasekara

The most critical decision our country is facing today is the topic of the The Island editorial of 19.08.2021 ‘To close or not to close’. The editorial discusses in its usual forthright manner the crucial issues that need to be considered with regard to keeping the country open or closing the country. However, as we have been witnessing around the world, (and as acknowledged in the editorial as well) the reality is that when push comes to shove, a lockdown is the only viable alternative. This article despite having a title that reads like ‘the lion, the witch and the wardrobe’ intends to present some of the scientific data that would need to be considered in deciding the timing of a lockdown.

A lotus leaf doubles in size every day. After 50 days it covers half the pond. How long will it take to cover the pond completely?

The R0 (pronounced R naught) is a value/ index, known as the basic reproduction number, that scientists use to determine how contagious an infectious disease is. R0 value tells us how many people will contract the disease from a single infected person. The higher the value, the more contagious the disease is. For example, Measles, which is notoriously contagious has a R0 value of 12 to 18, meaning one infected person will infect another 12 to 18. A R0 value of 1 means one person will spread it to another. So, ideally for an infectious disease to come under control its R0 value has to drop below 1.

Vaccination is the recognised definitive means to bring down the R0 value almost to zero, as immunising the vulnerable population helps get rid of the viable host, as has been the case with Polio, Measles, etc. Unfortunately, this does not seem to be the case with the current Covid-19 vaccinations. Though the benefit of the vaccine for an individual is undisputed, the impact of the vaccine in reducing the community spread of Covid-19 is yet to be determined.

In the absence of vaccination, the next step to bring down the R0 value is social distancing, wearing masks, washing hands, decontamination, etc. The ultimate step is a lockdown to bring the R0 value close to zero, where the virus’s chances of getting from one host to another are minimised as hosts are no longer allowed to interact with one another.

The important aspect that needs to be appreciated in the control of infectious diseases is that the case load progresses as a geometric sequence and not as an arithmetic sequence. Therefore, after a seemingly benign set of numbers, the numbers become alarmingly huge very quickly.

The answer to the lotus leaf question is ‘one day’. As it doubles every day, though it takes fifty days to cover half the pond, once it gets there, it only takes one more day to cover the pond completely. Readers with a mathematical bent would have worked out that the R0 value for the lotus leaf is 2.

Therefore, the critical question that needs to be answered is what the R0 value for the Covid -19 (in Sri Lanka) is. The initial value calculated by Dharmaratne et al, published in the journal of Virology in October 2020 (https://virologyj.biomedcentral.com/articles/10.1186/s12985-020-01411-0) was around 0.93 to 1.23. This however, included data up to the 30 April 2020, which covered the period that we were under a lockdown as well. I was not able to find another value after this publication. The article-‘Sterner action the need of the hour-Disaster in waiting’- by Prof. Ananda Jayasinghe, Professor of Community Medicine (Faculty of Medicine , Peradeniya) published in The Island, 14.08.2021 ‘quoting from the CDC’ suggests that the original Covid-19 variant had an R0 of 2, whereas the newer delta variant has an R0 closer to 5 ( https://www.cdc.gov/coronavirus/2019-ncov/variants/delta-variant.html.)

Currently, Sri Lanka has a case fatality rate of 1.7%. Many in the health sector, however, feel that we are not detecting the true number of cases due to inadequate testing and that in fact our true case load is much higher than what is detected. So, if we assume that there are more than twice as many cases, our true case fatality rate can be rounded to say 0.5 %. For 150 deaths that are recorded daily, there are 30,000 active cases. Taking the R0 value of 2 the progression of the case load from 30,000 to 60 to 120, to 240 to 480 to, 960 thousand and to 1.92 million, will take 6 cycles and another 3 cycles to get over 15 million. If, on the other hand, the R0 value is 5 as suggested, then from 30,000 to 150,000 to 750,000 to 3.75 million takes only 3 cycles, and another two more cycles will be beyond our population.

The other aspect that needs to be factored in is the speed with which the virus spreads. The current delta variant spreads faster than its predecessor. Research has indicated that a person who gets infected spreads the virus to another person after four days as regards the delta variant in comparison to six days for the original strain. (https://www.dailymail.co.uk/health/article-9815917/Indian-Delta-Covid-variant-spreads-fast-makes-copies-quickly.html.)

Therefore, the increased geometric sequence now gets further accelerated by an arithmetic sequence as well. To put it in context, during the time that the original Covid strain with a R0 of 2 gets from 30,000 to 120,000 (2 cycles), the delta variant with a R0 of 5 will go from 3,0000 to 3.75 million (3 cycles).

Therefore, if one is to take action that would be effective i.e. a lockdown, it needs to be done when one is handling a seemingly benign case load. This is why countries like New Zealand went into a level four lock down on the assumption that the isolated single case of Covid-19 could be a delta variant!