Written evidence submitted by Dr Marek Laskiewicz (CLL0033)
Title
Public Health Policy Issues with the Reproductive number R
Word Count from Introduction to Conclusion, hence without the Title Page, Acknoledgements and References (23 in all): 2992 words and a Summary Box of 113 words. The Abstract in the Title Page contains 91 words. There are no figures or tables.
Abstract
Objective: To reduce the negative non-medical especially economic consequences of a pandemic. Analysis: The Reproductive number R is important, but only a dependent variable, guide and average. So it should be used as a cross-check; policies should incorporate it in a formal benefit-cost analysis; auxiliary research ought to be carried out; and a mitigated lockdown should be implemented with scientific social distancing whereupon all activities including large gatherings observing this restriction could be permitted immediately. Conclusion: a mitigated lockdown ought to be considered in order to reduce the deleterious secondary pandemic consequences.
Summary Box
What is already known about this subject?
This paper is novel as it lies on the interface of medicine and social sciences so the first in its field. However it is by the same token partially based on epidemiology, notably the Reproductive number R, and social sciences notably economics.
What are the new findings?
It is a new analysis hence a new policy of how to cope with the secondary problems especially economic lockdown has caused without a negative impact upon the key medical problem of this virus. This hinges on a correct analysis of R as a dependent variable and on expanded utilisation of R, notably of estimated R’, benefit-costing and micro-R.
How might it impact on clinical practice in the foreseeable future?
There is no such direct impact. However the concept of auxiliary research does apply to it too.
MeSH Keywords
Basic Reproductive Number G03.850.505.400.975.525.080
Economic Models G03.850.520.830.500.600
Epidemiological Studies N06.850.520.450.500
Epidemiology H02.403.720.500
Public Health N01.400.550
Standard Keywords
Reproductive number R; public health policy; Covid-19; SARS-CoV-2; benefit-cost analysis; lockdown; pandemic; social distancing; mitigated lockdown; coronavirus economic consequences.
Introduction
The over-focusing on the epidemiological Reproductive number R is counterproductive for the national recovery from the Covid-19 (SARS-CoV-2) virus. It is of course a valuable number per se,[1] and public health policy planning must take it into account. However there are several issues and proposed improvements. This is important as in the future this virus, a mutation or a different one may strike, occasioning another pandemic, whereupon its secondary effects such as on the economy must be better managed.
The Reproductive number R is more accurately termed the effective Reproductive number Re:
R = Re in this paper.
Analysis
These issues are presented here. Instead of Methods and Results, these are analysed. The nation analysed is the United Kingdom, but the analysis applies to every nation in the world, indeed to the world as a whole.
R as Dependent Variable
R seems to have become for politicians and the media an end in itself, a determinant, whereas it is actually simply a reflection, a dependent variable, not an inherent characteristic of the pandemic. So the goal should be implementing advantageous lockdown relaxation policies in particular for the economy, with R acting as a cross-check; instead R qua end is (wrongly) publicly seen as the disease parameter which allows or blocks further lockdown lift, so (wrongly) treated as a brake, whence for example the ‘wiggle room’ stated in the media.[2]
However there is one aspect of R, its underlying virulence,[3] which is an independent variable. So its underlying virulence factor, being a function of its biochemistry, is ostensibly a determinant, though as nothing can be done about this, it is actually an independent variable that is only partially a policy determinant; this is the Reproductive number when there is zero herd immunity R0. However this does not per se appear to fluctuate,[4] hence acts as a constant, so can be ignored for short-term policy decisions since this is unaffected by them:
R = f(R0), ceteris paribus, where R0 = k for a given virus.
Were this virus to mutate, this virulence factor might alter. It has been determined as 5.7 for Covid-19:[5]
R0 = 5.7 where R = RCovid-19.
Similarly R might be affected by ambient temperature T, decreasing as this rises, hence an inverse relationship. This would produce the confusing effect of the virus seeming to be defeated, whereas it is merely an effect of the warmer climate such as over summer merely temporarily weakening it:
R = f(1/T) ceteris paribus.
Nonetheless the R value decrease would be welcomed and bring about a premature lockdown lift, whereas it would only be a temporary respite, as may be the case now. However the temperature cannot be controlled, it can only be taken into consideration or simply adapted to; in any case the evidence at present for a temperature effect or indeed any weather effect is inconclusive:[6] so this can be ignored in policy planning at present.
Thus R is simply a cross-check. Neither the inherent virulence factor nor the ambient temperature need be noted for a policy decision. So actually a high R implies that inadequate policies are being utilised, unless it can be shown that either the virulence factor has varied or that the virus is temperature dependent.
Moreover R is not the only medical or epidemiological consideration.
Furthermore R has varied over time as different policies P have been implemented so is actually Rt. So mathematically:
Rt = f(Px) ceteris paribus, where x = 1, 2, ….
As such it has a given value only at a certain time, so should always be reported with a time tag.
In addition it is then possible to present both the change in R, say from day to day, ΔR, and indeed theoretically the rate of change R/t.
R in Benefit-Cost Analyses
As R can be used as a cross-check, it follows that it could be used not only as an overall number but also as a policy-specific one.
Thus the Government should seek to implement lockdown relaxation policies that are R-neutral or ideally R-decreasing. Each policy should be R evaluated or at the very least estimated, and this number then presented.
Nonetheless R-increasing policies need not be rejected out of hand; they may be justified in that they reduce a secondary problem such as helping economic recovery; so such policies should be presented noting the R effect as well as their secondary benefit, again ideally quantified. This would allow a cost-benefit analysis, better termed a benefit-cost analysis for reasons presented below, here, say, an economic GNP benefit and a medical R cost to be presented; policies could then be ranked in these terms; indeed even R-neutral or R-decreasing policies could be so analysed and presented. In addition this would mean that policies and their effects could be monitored, though this would require statistical analyses such as economic by econometric analyses. This might result in some policies being postponed or rejected until a vaccine is available, whereupon full lockdown lift would finally be possible.
Moreover R-neutral and especially R-decreasing policies could then be implemented even though the overall R number for the UK was more than 1. Indeed it could be any number over 1 as long as the implemented policy was not greatly R-increasing. In short, economy versus epidemiology: the underlying problem in this outbreak. R qua determinant is blocking any consideration of these, so unnecessarily over-reducing the economy.
R’ and ΔR’
The above benefit-cost analysis ought to employ a slightly different variable, namely R’. This is because R ought to be reserved for actual measured historical values, hence a real R, so also for a scientifically determined prediction; whereas a benefit-cost analysis can also function with an estimated R effect, which may turn out different when implemented and subsequently measured, hence an estimated future value as opposed to a scientifically exact prediction, so better written as R’, whereupon no confusion would arise. Likewise for the co-variable, say, GNP [Gross National Product] which if estimated could be better presented as GNP’. This innovation is needed because any such analysis, such the potential R’ effect of crowded beaches in the future, is a theoretical construct, not an empirical assertion.[7]
Another innovation is needed as the co-variables are dissimilar: so both differences must be stated as proportions such as percentages and not in absolute terms in order to be able to compare the benefit with the cost, and against other policies. Such a differential benefit-cost analysis would thereupon function like a standard one.
A final innovation is then needed as the co-variables are dissimilar: their effects must be compared by dividing them hence as fractions instead of as a total by subtracting the cost from the benefit as usual. Thus it is better to employ the term benefit-cost for former and leave the term cost-benefit for the standard latter.
Consequently the benefit-cost analysis BCA could be carried out but would vary according to whether the lockdown regime is relaxing as at present or tightening. So the benefit for the economy ΔGNP’ at a given ΔR’ cost during lockdown relaxation for a policy Px could be determined and compared with other options:
BCAPx = ΔGNP’/ΔR’ where Δ is the estimated percentage Increase.
Conversely the benefit-cost analysis for the economy during lockdown imposition, which may yet re-occur,[8] for a policy Py could be determined and compared with other options:
BCAPy = -ΔR’/-ΔGNP’ as both co-variables are decreasing.
In both lockdown regimes there would be a set of outcomes which could ranked, so that those with the highest benefit-cost could be selected. Indeed more than one policy, hence the better ones, could be so selected and simultaneously implemented.
Such sets of outcomes could include cases where both are negative for the former or positive for the latter lockdown regime.
Actually this analysis is more complicated because R’ might be neutral for a policy, so this would need a separate set of outcomes, as a paired set or ratio as opposed to as a fraction; indeed this would be a better way of presenting all BCA outcomes. Theoretically another set is needed if there is a benefit and the cost is actually beneficial too, hence negative, though this is ignorable.
It need not be the economy that is the co-variable. However other potential co-variables such as civil liberties are hard to quantify; in any case an amelioration in one secondary problem such as economic would also be reflected to some degree in others such as civil liberties.
Mitigated Lockdown
A high R value qua problem does admit of a different practical solution than full lockdown; as such R is a guide, a very valuable one, arguably the most important. ‘Mitigated lockdown’[9] is proposed instead; this is lockdown based on social distancing with all activities permitted, though it is stressed permitted only providing social distancing is observed. This would suffice; for the disease mechanism is known so full lockdown is an overreaction. There is in fact no difference in where the social distancing is observed, notably whether in essential or non-essential work, providing it be observed; indeed there is no theoretical difference in how many so work or for that matter play. Thus the R number for the nation will not be altered whether few or many are permitted to work (or whatever) under social distancing; however in full lockdown the former has been chosen hence only a few, essential workers can go to work, and only to work; yet the economic benefits of the latter in mitigated lockdown are enormous. Therefore all businesses including all shops and restaurants, all travel and hospitality services, all organisations including all churches and universities and all social events such as football matches, indeed all activities should be permitted – but within the limitations set by social distancing, isolating and testing as primarily determined by medical advice, hence without any economic, political or sociological considerations as these are secondary problems. Such activities are therefore R-neutral.
Now social distancing ds can be controlled, hence R can be reduced whatever the underlying virulence factor of any virus. It is an inverse relationship:
Rt’ = f(1/ds) ceteris paribus.
Here the relationship is not linear, rapidly falling off with social distancing:
Rt’ = f(1/dsz) ceteris paribus where z > 1.[10]
Thus a reduction in R to below 1·0 was and is achievable without a full lockdown. This is true even in the absence of a vaccine.
In addition mitigated lockdown should be also be considered in future should a new Covid-19 wave arise, or a mutation or a new virus. There is no need for the world to shut down with the huge concomitant economic, political, social and cultural cost.
Mitigated lockdown could also be applied worldwide; for the UK is not of course alone in its coronavirus sufferings. Thus it comprises permitting all R-neutral and R-decreasing lockdown relaxations so that the effect on secondary problems such as political, can be reduced to the lowest level compatible with epidemiological safety, ideally a subunitary R number.
R as Average
R is only an average, albeit down to regional level. As such it does not reveal local problems: these would be measured by a micro-R, Rμ; and in BCA analyses, this could be an estimated micro-R, R’μ.
Micro-R
So R qua average hides the fact that for example groups of strangers meeting or simply being too close in, say, a park will potentially have a high R’μ, maybe well above 1·0, yet the park as a whole a low R’, maybe less than 1·0, since the vast majority of visitors observe social distancing. Thus the emphasis should be on social distancing between several strangers, instead of on the activity or the overall R number – which were this policy followed, would in fact eventually fall because potential high R’μ hotspots would be eliminated.
Therefore it is not that lockdown relaxation now is wrong per se; actually it is too limited according to the above analysis, and arguably being implemented by non-medical considerations. Rather the problem is that social distancing is not being adhered to always everywhere, witness the recent demonstrations; and this problem may grow if the lockdown lift is not introduced properly. This may result in the R value increasing with the associated rise in Coronavirus cases: indeed the gains made by full lockdown may be subsequently jeopardised. So what is needed is a continuation of lockdown, albeit a mitigated version – not a free-for-all.
Likewise the above analyses also apply should it be necessary to re-impose lockdown because the R number is much higher than one. Again a benefit-cost analysis of various lockdown policy options could be drawn up. Indeed lockdown return should be being considered now as it is likely a second bout of Covid-19 will appear, especially if there is continual social indiscipline.[11]
This solution also allows large mitigated gatherings, so no limits exist providing there is social distancing, especially when there is also hand sanitising or masks or both, so there is really no reason why, say, concerts and sports grounds could not be opened within these strictures. Anyway the scientific case against large, temporary gatherings is unclear.[12] Therefore R is a function of a social distancing and interaction time tI:
Rt’ = f(1/dsz,tI) ceteris paribus where z > 1.
Auxiliary Research
As part of mitigated lockdown, ‘auxiliary research’[13] is also proposed. This research does not try to cure the disease, so is not main research such as that by PHE, but simply sets out to alleviate the secondary problems. In particular the scientifically correct social distancing must be established[14] and the questions surrounding large gatherings resolved.[15] Such research would enable the nation and indeed the world to cope better with the secondary problems. This must be based on science as opposed to opinion; for no matter how expert, in the philosophy of science it intrinsically remains but an opinion.
Therefore this auxiliary research would include economic-medical studies.
Such research would be complicated. It is proposed here that social distancing should be location-dependent. So there will be more than one social distancing, indeed a multiplicity thereof depending upon the circumstances, specifically the location L, notably for outdoors, normal indoors, disciplined indoors such as factories where it might be smaller, and confined indoors such as restaurants where it might be greater,[16] greater still with vulnerable people hence in care homes and hospitals, and even greater in some places therein. Thus the current uniform social distancing, being a simple one-size-fits-all should be amended. Moreover it is proposed that such research should investigate the potentially beneficial effect of increasing the room air changes by means of complex ventilation, especially for disciplined and confined spaces, which might consequently reduce such social distancing; this could be implemented legally by amending the Building Regulations, supplemented by ACOPs.[17] Furthermore social distancing would vary according to the reported national R, so the previous R, ie Rt-1; for although in principle it is independent of this as stated above, in practise it may not be perfectly observed whereupon a larger social distancing might well be safer. Likewise social distancing should vary according to vulnerability V, hence the old or ill might well maintain two metres or more whereas those younger less if the research so proposes. Thus social distancing would be location-R-vulnerability dependent:
ds = f(L,Rt-1,V).
A public inquiry should also be started set up now. It should publish interim reports; for the virus might take a long time to be finally subdued.
It is stressed that auxiliary research should not be regarded in any way as a substitute for main research,[18] but rather as complementary.
R reviewed
Nevertheless none of this is to suggest that R be abandoned or that it is unimportant; on the contrary it is the most important parameter of all. Likewise the medical danger of this Coronavirus remains of paramount concern; for other problems generated by lockdown are secondary.
Rather it is that R is being incorrectly utilised for public health policy. So it should be expanded into estimated R’, benefit-cost studies and micro-monitoring.
Moreover according to this analysis, the current sudden big jump from 2m to 1m social distancing[19] when the underlying science has not changed and there is no vaccine (and worldwide cases are still increasing[20]) may well prove counterproductive, there being a risk it might help bring about a second wave; and only some more businesses were permitted to operate. Instead all activities including all businesses should have been permitted but within scientific social distancing, which would have been a potentially safer medical-economic option; indeed this could have been done from March instead of full lockdown, and should be done should a second wave strike.
Discussion
The main finding of this study is that all activities should be permitted subject to social distancing being maintained at all times. This mitigated lockdown instead of a full lockdown should also be reintroduced if this virus, a mutation or a new one appears in force later.
R is widely known and presented continually. However as the ideas in this paper are new, albeit having been broached earlier this year,[21] little is known in the context of secondary problems occasioned by this virus, except for standard reports as in the economic effect, in particular little stated how to combat them – and this is potentially dangerous since there is political pressure to decrease social distancing by fiat not science. Thus auxiliary research should be formally set up.
The limitations of this study are that the virus per se is not considered, notably neither its medical aspects, nor its background biological details notably its biochemical structure and modus operandi, nor its vaccine. It concentrates solely on public health policy in the context of reducing the non-medical impact of the virus, such as on the economy, to a minimum compatible with medical safety, which it stresses must not be compromised on the grounds of expediency.
Acknowledgements
As no experiments were carried out, no ethical approval or patient consent was needed or sought. There is no additional data. The Research Checklist is not applicable.
Likewise no funding for this paper was either sought or received. The author has no competing interests. The author is the sole contributor: there are no co-authors.
Conclusion
Mitigated lockdown based on a correct, expanded use of R is ultimately necessary lest the cost of defeating the disease prove exorbitant - roughly £51B increase in the National Debt in April (£62B in all)[22]and estimated to rise to an extra £240B (£298B in all).[23] It would be a sad irony if the pandemic was defeated, only to find that the economy, which is surely also important, was ruined. Likewise for every nation in the world. Especially if there arises a second wave, or a new virus.
References
1 See Ferguson, N. et al, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, on behalf of the Imperial College COVID-19 Response Team, WHO Collaborating Centre for Infectious Disease Modelling, MRC Centre for Global Infectious Disease Analysis, Abdul Latif Jameel Institute for Disease and Emergency Analytics Imperial College London, 16-03-2020, ret. 20/4/2020.
2 E.g. Whipple, T., Coronavirus spread: Rising infection rate prompts warning of second wave, The Times, London, 16-05-2020; recently health leaders called to be prepared for this, see Open letter, Covid-19: Call for a rapid forward looking review of the UK’s preparedness for a second wave, BMJ, London, 23-06-2020, ret. 24-06-2020.
3 See Etiology section, Ye Yi et al, Covid-19: what has been learned and to be learned about the novel coronavirus disease, International Journal of Biological Sciences, Sydney, 16-03-2020, ret. 14-06-2020.
4 Recent claims by Prof. A. Zingrillo that Covid-19 is weakening have been dismissed, see Kelland, K. & Parodi, E., WHO and other experts say no evidence of coronavirus losing potency, Reuters, London, 01-06-2020, ret. 21-06-2020, hence it is not fluctuating.
5 See p.1, Sanche, S. et al, High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2, Emerging Infectious Diseases, CDC, Washington, July 2020, ret. 22-06-2020, though others state 2.2, see Transmission section, Note 3.
6 See Lawton, G.,Will the spread of covid-19 be affected by changing seasons?, New Scientist, London, 01-02-2020, ret. 21-06-2020, yet other studies show a weak negative correlation with temperature, see Mandal, C. & Panwar, M., Can summer temperatures reduce Covid-19 cases?, Public Health, London, August 2020, ret. 24-06-2020.
7 There is no evidence for the spread of Covid-19 on the May Bank Holiday (cf Note 11).
8 As envisaged from lockdown start, see p.16, Note 1.
9 See Ch. 21.2-11, Laskiewicz. M., Covid-19 Lockdown Analysis, Krzenwic, London 2020.
10 Notably at 2m it is 10-30 times less likely than at 1m, see p.4 & p.9, Scientific Advisory Group for Emergencies [SAGE] – Environmental Modelling Group [EMG], Environmental Evidence on Transmission, London, 26-05-2020, ret. 22-06-2020; also important is a study confirming that less than 1m is dangerous, see p.9, Chu, D. et al, Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis, on behalf of the COVID-19 Systematic Urgent Review Group Effort (SURGE) study, The Lancet, London, 01-06-2020, ret. 20-06-2020.
11 See, eg. People urged to stay away from UK beaches over sunny bank holiday weekend amid social distancing fears, ITV Report, 23-05-2020, ret. 10-06-2020.
12 See p.6, Note 1 & SPI-M-O: Consensus view on public gatherings, SAGE, London, 11-02-2020, ret. 30-05-2020.
13 See Ch. 22.3, Note 3.
14 As by SAGE; there have been others such as by Chu, D. et all, see Note 10; also Social Distancing Research Proposal by Laskiewicz, M., submitted to UK Research and Innovation [UKRI] on 28-05-2020.
15 See Note 13.
16 Idem; much research work about simple social distancing and other actions such as mask-wearing and hand-sanitising has been carried out, see pp.12-24, SAGE-EMG, Transmission of SARS-CoV-2 and Mitigating Measures, London, 12-06-2020, ret. 19-06-2020.
17 As for Legionella there is ACOP L8 – HSE, Legionnaires’ disease. The control of legionella bacteria in water systems, 4th ed., London 2013; HSE also issues further documents such as HSG 274 for legionella.
18 Such as that referenced here, eg. Notes 3, 5 & 10; there is of course much work elsewhere, eg. see Clarke, M. et al, Establishing prison-led contact tracing to prevent outbreaks of Covid-19 in prisons in Ireland, Journal of Public Health, Oxford, 22-06-2020, ret. 23-06-2020.
19 See Stewart, H., Boris Johnson ditches 2m physical distancing rule in England for ‘1m-plus’, The Guardian, London, 23-06-2020.
20 See DW News [Deutsche Welle], Coronavirus: WHO reports record daily increase in global cases, Bonn,
22-06-2020, ret. 24-0-2020.
21 See Note 9.
22 See Ch. 2, Public Sector Finances, UK, Office for National Statistics [ONS], London, April 2020.
23 See Coronavirus Analysis, Office for Budgetary Responsibility, London, 14-05-2020; it is rising now, see Nawan, G., National debt now bigger than economy, The Times, London, 20-06-2020.