Prologue: Ever since the present COVID pandemic unleashed its fury on mankind, an extremely important figure essential for planning the various public health control measures and for visualizing the possible future course has been the “Basic Reproduction Number”, abbreviated as “R0”. Various models for projecting the future course of the epidemic developed till now, have taken the assumed R0 as an indispensable variable in their calculations.
What is “R0”: R0 is defined as “the number of cases which will be produced by one single case in a purely susceptible population”. To simplify, it means that if the R0 of a disease is 3, and the average time taken by one case, from the point of his or her getting the infection till the point of time at which his “communicability” finishes (i.e., he / she is thereafter not able to further infect others) is 10 days, then in 10 days, this one case will lead to 3 cases and in the next 10 days, these 3 cases will result into 9 cases, and in the next 10 days, there will be 27 cases, and so on. If R0 is one, then 1 case will lead to one case in 10 days and this one case will lead to another 1 case in the next 10 days; thus the disease will be maintained at a constant level in the population. Lastly, if R0 is 0.8, then 100 cases will produce 80 cases in 10 days and these 80 cases with produce 64 cases in the further next 10 days; thus the diseases will be on its way to extermination.
Current position regarding estimates of R0: The estimated R0 in various models are based on certain mathematical calculations as well as on certain individual assumptions / guess-works. Various workers and organizations including WHO, have put their “guesstimates” of R0 from as low as 1.2 to as high as 4.20. While the difference between 1.2 and 4.2 may appear to be trivial, but in real public health and epidemiological practice it makes a huge difference as would be apparent from the following hypothetical example:
Let us say we have one Lakh detected cases of COVID-19 today. So, what is our estimate about the number of cases after 70 days? Now, let us assume that the “median” period of the time between acquiring the infection till the point that he / she is no more able to further transmit the infection to other human beings is 7 days for a particular infectious disease (unarguably, many cases will have higher period and many will have much lower, but on an average, for large scale calculations, the median will be a correct number to proceed). So, one transmission cycle will be completed in 7 days and 10 transmission cycles will be completed in 70 days. Now, if we assume that the R0 is 1.1, then, given that the number of cases are one lac today, the total number would work out to 2.6 lakh after 10 weeks. On the other hand, if the R0 is 2.75, then the one lakh cases today would expand to 247 Crores after 10 weeks. Such is the difference that even minuscule looking variation in R0 is going to make.
Methodology used for calculating the R0 for our country:
- Data was obtained from the official / reputed sites in respect of our country (ICMR site for tests undertaken, Aarogya Setu and Worldometer for day wise Total cases / Total deaths / Total active cases / Total recovered cases.
- It was assumed, based on various descriptions of SARS-Cov-2 epidemiology given by experts, that the median incubation period of the disease is 7 days. Some cases will have a higher incubation period while some will have smaller incubation period but for public health and epidemiological purposes, 7 days can be taken as a reliable estimate.
- It was also assumed that in the very large majority of cases, communicability (i.e, ability to transmit the diseases to others) is from 2 days before to 2 days after the onset of symptoms, i.e., it would be, on a long term average, from 5 to 9 days from entry of infection. Thus, one transmission cycle is likely to be completed in maximum of 9 days.
- 8th May was taken as the start point since by then, 6 weeks of national lock-down (which was made effective from 25th March) was completed. This also meant that three maximum incubation periods (of 14 days each) had passed since the declaration of nation-wide lock-down and hence, stability in transmission would have been achieved after implementation of the lock-down.
- It was also assumed that while the number of cases officially detected were 56342 on 8th May, however, due to low level of testing facilities (testing rate was only 1143 tests per million population on 8th May), the actual symptomatic cases would be 4 times this number, since many could not have been tested. Thus actual number of symptomatic persons is therefore likely to have been 2,25,368, country-wide. Now, since 85% out of all the infected are likely to remain asymptomatic (and hence having a very low probability of being tested), the actual number of infected on 8th May is likely to have been (225368 * 100) / 15 = 15,02, 453.
- On 31st July (84 days after 8th May), the officially detected cases were 16,97,054. However, since the testing rate had increased by nearly 12 times on this date as compared to 8th May, we can assume that the total number of actual symptomatics would have been 2 times (and not 4 times as assumed for 8th May). Thus, the total number of symptomatic persons would have been 3394108. Again, since this figure would have constituted the “asymptomatics”, the total number of infected would have been (3394108 * 100) / 15 = 2,26,27,387.
- By placing these figures into a mathematic model, with the baseline figure as 15,02,453, the present figure as 2,26,27,387, the total duration as 84 days (i.e., 9 transmission cycles plus another 3 days to cater to any outlier), the R0 was worked out, using a statistical calculator.
Result: Using the above methodology, the R0 works out to 1.31
Implications: The above figure of R0 = 1.31 may appear to be trivial. However, it may have far reaching implications. If the current socio-economic, demographic and disease dynamic conditions are going to be stable for the next 6 months (which are likely to be, since we are not likely to get any vaccine for mass usage, any major break-through in patient management modalities, any further nation-wide lock-down, or any other significant mass migration of population in the next six months), then with R0 of 1.31, in the next six months:
- The number of cases detected as positive on testing may run into into single-digit figure of crores,
- The actual population infected may run into a few scores of crores, and,
- The total deaths may cross the million mark.
So, What can we do now: I suggest the following measures:
- To make use of masks legally compulsory, excepting when inside the home
- To keep strict ban on “economically non-productive” mass congregations, as religious fairs / festivals, Spectator-based sports events, cultural / social congregations, and so on.
- To develop/ strengthen the healthcare system to deal with the large influx of “severe” / “critical” cases likely to come up in next few months
- To treat the mild and moderate cases at home; reserve the hospital resources for serious / critical cases, which are likely to come up in large numbers and may overwhelm the healthcare capabilities
- To make testing available to the maximum capacity
- To test only the “symptomatics”, using “point of care diagnostic tests”
- To STOP straining healthcare as well as administrative manpower for “tracking – testing – quarantining” of the contacts; it may not give results commensurate with the inputs, in the face of an overwhelming epidemic. It was a good strategy when the epidemic had just started and may be again a good strategy when the epidemic is on its way down but for now, it may not be the strategy at all. We also need to conserve the healthcare manpower for dealing with the possible oncoming large influx of patients.
I would look forward to having your kind inputs. Regards,
Air Vice Marshal (Retd) Dr Rajvir Bhalwar
MBBS (Lko); MD (Public Hlth / Preventive Med) (Pune); PhD (Public Hlth / Preventive Med) (Pune); FAMS
Post Doctoral Fellowship Training (Epidemiology) (INCLEN)
PG Dip Hosp Adm (Del); PG Dip Med Laws (NLS Bangalore)
Dean, Rural Medical College
Pravara Institute of Medical Sciences (Deemed University)