Covid 19: Did lockdown work?

Science progresses by making and testing hypotheses. Often principles, practices or policies which look sound at one level get falsified at later stage when examined with more data. Rethinking and re-examining well accepted norms is an important part of science, failing science becomes a religion. In March 2020, when the threat of the pandemic was suddenly realized, it was inevitable to suggest and implement a set of measures to arrest the transmission and things that looked logical that time were suggested and implemented. As time passed, data started pouring in and in the light of the data it was necessary to re-examine what was working and what not. It was stupidity to expect that the same things would work all over the world given the wide variety of contexts and conditions. So according to data getting accumulated, the policies should have been re-examined, refined to suit local contexts and withdrawn if found useless. This process should have started by May or June 2020 itself as data started accumulating.

Although delayed substantially, the process of introspection appears to have begun now, at least in a small way. Two papers last week appearing in NEJM and BMJ reexamined school closure as one of the measures to arrest the epidemic. The study in Swedish schools that did not shut down shows no evidence of higher rates of illness among students and teachers in schools that remained open. The other Belgian study says that the negative impact of school closure on kids appears to outweigh the weak evidence that closing the schools might have actually reduced transmission. We need more such data based introspections and re-appraisals of every policy. This analysis might help us at least the next time a new respiratory virus appears.

I am examining below the possible impact on the spread of infection of implementing lockdowns, lifting of it and undue crowding of people without taking necessary precautions. We have ample opportunities to examine the actual impact of crowding without following the necessary norms. In October and early November there were elections in Bihar which were accompanied by large public meetings, rallies and celebrations by the winning candidates. In the following month there were elections in Jammu and Kashmir which in some areas showed record voter turnout. From late November farmer agitation started on an unprecedented scale with huge processions and gatherings which have continued for three months now.

An epidemic follows a typical shape of the curve when plotted daily or cumulatively. If lockdowns really worked we should see at least a temporary downward shift in the slope, especially on a log scale. Conversely whenever restrictions were lifted or there was large scale crowding, there should be a local upward movement of the curve. Here are the time trends plotted along with the dates on which restrictions were imposed or lifted, election campaigns, rallies, big meetings or celebrations were conducted. The upper curves are cumulative incidence on log scale, lower curves daily new cases (7 day running average) on linear scale. All data taken from

The nation wide trend: See that lockdown did not decrease the slope and the unlock or crowding events did not increase it. The peak in the daily incidence trend and the following downward trend appears to be independent of all these events.

The Kisan Andolan should have theoretically been the ideal occasion for spreading the infection. But there appears to be no increase in the incidence in Delhi, nor in Punjab and Haryana (below).

Overall, the shape of the cumulative trend appears almost unaffected by any of these events when examined at national or state level. The daily trend has many ups and downs which have no association with the events of crowding and norm violation, even after allowing realistic time lag. So in regional or national time trend, there is no evidence of either the lockdown having improved, nor of crowding and norm violation having worsened the situation.

An epidemic is a complex phenomenon and just owing to its complexity, it’s no surprise that some simple minded solution might have failed to work. If some policy did not work as expected, it should not be taken to mean ignorance, stupidity, failure or lack of foresight of the policy maker. We just need to accept that this measure did not work and plan alternative measures that are likely to work better. But the inability to accept that something failed at least in some specific context, is the sign of being dogmatic. If lockdowns have not worked in the Indian context so far, it makes no sense to have them again if faced with some local  surges. Saying that it worked in New Zealand has no relevance. Inability to learn from data is a sign of not understanding science and not being ready to use it appropriately. The top level Indian science organizations and health authorities need to give at least some proof that they also learn from data and rethink, re-examine and refine the policies in response to observed data. Otherwise there will be no difference in the approach to build a Ram temple and the approach to curb the epidemic. One is clearly a religious issue, but the other is expected to be scientific. So let the latter be evidence based rather than faith based.

Logic versus number: What scientists value more?

Science has a set of principles and the attempt is to achieve as many of them as possible, although not in every study all the principles can be complied to. For example, a famous Lord Kelvin quote says, “When you can measure something you are talking about and express it in numbers, you know something about it.”. At times some important factors are not objectively measurable and then one has to settle either on a qualitative analysis, or use some surrogate marker etc. This is an inevitable limitation at times but I don’t consider this as a major issue in the scientific method.

A trickier situation is when two principles are in direct conflict. If you try to achieve one, you need to compromise on the other. The interesting question is what do we do when there is such a conflict? The question is not restricted to one researcher’s decision. In today’s scientific publishing system, it should be acceptable to the reviewer. Only then you can publish. How frequently a conflict of principles can arise? I don’t know, because this question wasn’t there in my mind until recently. I have at least one example of such a conflict now, which opens up a new subtle but important question in the philosophy and methods of science.

Over the last few years I am increasingly getting interested in how common people use innate statistical analysis to make inferences from their own sampling and observations. To some extent this question is considered by Bayesian statistics, but my question is much broader and many aspects of which are not covered by Bayesian statistics. One such question we attempted answering using a small experiment is uploaded as a preprint now, but not yet published (doi: 10.20944/preprints202012.0200.v1).

Another thing I wonder about is, what do people do to make a dichotomous decision based upon their own sampling/observations? In formal statistics we have a concept of statistical significance, which is used to make a dichotomous inference by taking an arbitrary cut off level of significance. The most commonly used significance level of 0.05 is arbitrary but well accepted. I am trying to observe at what level people make an inference? For example, when do I decide that this cap is lucky for me? How many times a favorable event needs to be associated with that cap so that my mind considers that cap as lucky? What I feel currently is that we keep this level variable depending upon the cost of making a wrong inference versus the benefit of being correct. In this case, being particular about wearing a certain cap has a small cost. Being successful in an exam, for example, is a big gain. So if I make a wrong inference of a significant association or actually causation, I have little to lose. If the association/causation turns out to be true, I have a big gain. So the cut off for making this association will be kept very liberal. This is how and why our mind keeps on generating many minor superstitions. It is a very logical and clearly adaptive tendency of the mind.

My real question begins here. It is most logical to keep the significance level variable depending upon the cost and benefits of right versus wrong decisions. Then why do we have an almost universal significance cut off as 0.05? In principle, statistical theory allows you to make the cut off more stringent or liberal depending upon the context. But hardly any researcher uses this facility; 0.05 has an almost religious sanctity. Why don’t we consider the significance level a function of the cost-benefits of an inference?

I don’t have a final answer but I am tempted to believe in this. The cost benefits are seldom objectively measurable. Most often they are value laden judgments. Two persons’ value judgment need not be identical. So it is difficult to arrive at a new agreed alpha appropriate for every context. Often people might agree that going wrong will be costly in this context, but exactly how costly can only be a subjective judgment. They may not have any precise numbers to agree upon.

We tend to avoid this loss of objectivity by compromising with the logically sound concept that significance level should be a function of the cost-benefit of decision. The level 0.05 is no way more sound than any one’s cost-benefit or value judgment. But it is precise, it’s a number, it has precedence and others, particularly your reviewers are unlikely to object to it. So we prefer being precise over being logical. This is a clear case of conflict between two scientific principles and almost universally we have preferred to be precise and numerical, at the cost of being more logical. Are there more examples of such a conflict or trade-off between scientific principles? I feel we are quite likely to see more. I have absolutely no idea whether philosophers of science have elaborated on any such trade offs.

At least on this issue, I feel the innate statistics of illiterate people may be more fuzzy bit still is more sound than the scholarly statistics to be found in the big textbooks and expensive statistical software. But they are illiterate after all and are not supposed to know the scientific method!! To me this is one more example demonstrating that science has much to learn from illiterate people. They are more logical in changing the significance level by the cost-benefit judgment. Mainstream science is more stupid for insisting on precision, on numbers, on consensus and that results into a religious significance cut-off.

Indian scientists not allowed to think novel – Current Science

Right at the onset I must say that this is not a criticism of Current Science. Current Science is an extremely valuable journal. Science publishing today is increasingly being monopolized by a few publishing giants. They charge the readers heavily and a big controversy over free access to knowledge is currently on fire. But what is even more weird is that they charge the scientists heavily to publish their papers. I have been briefly in the fields of performing arts, theatre and literature in my life. In all these field every contribution is remunerated, in a small or big way. When I talk about an author having to pay, my non-scientist friends just can’t believe!! This can’t be anything else but scandal, they feel. Science is the only field where a contributor has to pay for contribution to knowledge!! But the publishing giants have successfully made this a norm. Most interestingly, scientists (including myself) are the most stupid, helpless and gullible people to fall prey to this utter non-sense.

In this desert of stupidity, journals like Current Science are the last surviving oases. They neither charge the author, nor the online reader. They are run by the academies of scientists using public money. This is a great service and journals like this need to survive the global downfall of ethics in science publishing. Recently I got a weird experience with Current Science, which reflects more on the mindset of the mainstream community of Indian researchers, rather than reflecting on Current Science itself. As a common man and science lover, it is my duty to make this incident public.

To relate the story briefly, with two coauthors, one being a college teacher and another, a first year student, I communicated a paper to CS. In this we had used a simple mathematical expression that we thought works well as an index to reflect a pattern of our interest. Then there were a number of statistical arguments based on it. In due course of time the review response was received. There were comments by only one reviewer. His main objection was that this ratio had not been used before. There was no precedence and therefore we couldn’t use it. Any inferences based on a new index were not valid according to him. There was no other objection about the use of the ratio. He did not say anything about the ratio not being appropriate to answer the question addressed, the ratio having some undesirable properties that could lead to a bias or anything of that sort. His only objection was that there was no precedence of using such an expression so our entire argument was invalid!! Then there were a few other comments which we thought we could reply to or incorporate changes in the manuscript. In the reply, we added a supplement exploring the mathematical and statistical properties of the new index, ran simulations to show how the ratio behaves and argued that it was appropriate to serve the purpose. It would have been a fair rejection if he argued against the ratio with some logic, mathematics or statistics in support, if he thought our simulations were inadequate to prove our point and so on. He could have also said, whenever you are using a new expression, you need to be more careful. You need to do this, this and this before you bring it to a publishable level. This would have been a scientific and useful debate. Independent of agreeing or disagreeing, I would certainly have respected it. I really enjoy such debates. But no! On seeing the revision (or perhaps not even seeing it) he said again that you cannot use an index that does not have a precedence. He also said that our paper contradicted some recently published papers (without citing any paper) therefore our argument was flawed. There was no other reason given why he thought our argument was flawed.

In brief you cannot talk about anything that established scientists have not said before, forget about contradicting them!! The manuscript was ultimately rejected based on the single reviewer’s recommendation. Acceptance or rejection is not the issue here at all. All researchers know that it is a part of the game. It is not always logical. Subjectivity in the decision is inevitable. Chance plays a great role. But what is important is the basis on which a rejection is recommended. It simply means that introducing any new concept in science is only a monopoly of a few elites. Lesser mortals like you are not allowed to talk about anything new.

I wrote to the handling editor, keeping other editors in cc whether by the current science norms, not having precedence and contradicting earlier publications was considered a sufficient reason to reject a paper. A lot of correspondence followed. Most of it was either about the rejection, either justifying it or consoling us. But we had never challenged this particular rejection. This specific question whether not having precedence can be a valid reason for rejection did not receive a clear answer. The entire editorial correspondence is available for interested readers here ( The reviewer’s comments, our replies ( and the original and revised manuscript is available here ( Readers can make their own judgment.

In India, this is not the first time that such a thing is being experienced. Whenever something really novel comes from India, people look at it with suspicion. If something comes from the west, they generally have no problem. The modal Indian science community is still largely in the slavery days. Colonial era hasn’t yet ended. White man is still the master in the field of science. In India you may do some fill in the blanks kind of work, add marginal novelty for the name sake but Indians are not supposed to pioneer anything entirely new, small or large. It will not be considered science unless there is a white skin stamp on it. We recognize Indian scientists only by the honors they might get in the western scientific world. There are many science academies in India whose fellows are the most renowned researchers. These academies have several excellent journals such as CS. But the academy fellows themselves are always looking for publishing in the western journals with high impact factors. Publishing in an Indian journal is below their dignity, or only the last option if no western journal accepts their papers. One who does not do a post doc abroad is not worth even considering a scientist!!

About 20 years ago a senior scientist told me that he wanted to nominate me for Bhatnagar Award. Being just a science teacher, I did not expect this. Bhatnagar is not meant for science teachers. But to respect him, I provided the list of my papers and all other information needed. At that time I had published in PNAS, Lancet, Amercan Naturalist among others. But two of what I considered my best papers were published in CS. So in the list of my five most important papers I listed the CS papers with priority. One scientist who was on the Bhatnagar selection committee then, told me years later that when the committee members saw Current Science papers in the best paper list, within seconds my nomination was discarded. They didn’t even read anything further. In order to call it a good paper it has to be published in Nature, Science, Cell! How can an Indian journal paper be considered for  a Bhatnagar? Fellows of the Academies do not believe in their own journal! This is the level of self esteem of Indian Science. How can we expect path breaking work coming from India? Whenever it actually does, it is entirely the greatness of that exceptional individual, without community support, or in fact, is spite of the community.

On the other extreme are the fanatics of ancient Indian science. They are equally bad, if not worse, for the progress of Indian science. They think that all of Indian science happened thousands of years ago and now nothing is left to be done. So either way, there is no support for novel ideas originating from India. If you are doing science in India, and want to make a successful career, you should not seek too much of novelty. It is not allowed by other Indians. Originality makes life harder. Live a simple life and be successful by being a follower. You are not allowed to be a pioneer in this country. What happened with the CS review was only an inevitable reflection of the mindset of mainstream scientists in India. Therefore I don’t see any particular editor or reviewer being “wrong”. No individual in particular can be blamed because it is a community characteristic influencing individual behaviour. Rejecting originality by an Indian is the norm in Indian science. Only a handful might be exceptions. In such a community, what else can we expect?

Are clinical trials relevant?

I happened to read two things on the same day. One was some post on social media that said Remdesivir is not effective. I don’t believe on such posts immediately so I looked for the original paper. It was a Lancet paper describing a multi centre clinical trial of Remdesivir which found no beneficial effect on Covid-19 patients. Within a few hours I came across a newspaper carrying a two column news with a picture of people demonstrating on streets demanding Remdesivir be made available. The background is that Remdesivir has been among the costliest drugs for the treatment of Covid. It’s being sold in black for tens of thousands of rupees per dose. People want to buy it desperately, obviously because their physicians prescribed.

I then looked for more published clinical trials of Remdesivir to find that two more peer reviewed publications had said that there was no effect, and two said there was some effect. It’s not new that different clinical trials have somewhat different results. This is possible by chance alone plus there are subtle differences in the trial design, randomization protocols used, patient groups, the locally prevalent genotype of the virus and so on. Such differences are common when the effects are marginal. In such cases factors like conflicts of interest, conformity bias, publication bias suddenly become extremely important. For any drug that is extremely effective, different trials may differ slightly in the magnitude of the effect, but all are unanimous about there being a significant effect. For such cases conflicts of interest and biases do not interfere much. Anything that is really effective gets unanimous support of trials. Anything that does not have consistent support across studies, has doubtful and at the most edge effects. Putting all the trials together, it is clear that Remdesivir does not make a convincing case, at the most it may have marginal benefits.

So why are people paying such a high price for a drug whose effects are doubtful? A simple behavioural reason is that when there is no good choice, people go for the best among the bad choices. The meaning of ‘best’ here is not a scientifically tested ‘best’, it is the one which is marketed most aggressively or most tactfully. I was not surprised when I realized what is happening with Remdesivir, because I have seen the same thing has been happening with diabetes (type 2) drugs.

No clinical trial has shown that normalizing blood sugar with any drug can arrest diabetic complications. Trials like UKPDS and ADVANCE showed some marginal benefits of treatment. On the other hand, trials like ACCORD and NICE sugar trial showed that mortality is higher in the carefully sugar controlled group as compared to the moderately controlled group. Further there were many obvious flaws in the study design of the trials that showed marginal positive effects. For example, UKPDS, which is said to be so far the most successful trial to claim some positive effects,  did not have any placebo control group. In a disease like diabetes, there are two levels of possible placebo effects. A placebo effect means getting better just by the belief or feeling of getting better. One is the feeling that I am being treated. This can be controlled easily by having a control group with blank pills. The other level is the feeling that “Oh, my sugar is normal now!” Some positive physiological effects are possible because of this feeling alone. To control for this second level placebo, one needs to have a group which is not treated with hypoglycemic drugs but who are made to believe that their blood sugar is normalized. Such a placebo control has never been kept by any of the clinical trials. So the chance that the marginal positive effects that a trial showed are only because of this feeling, is never eliminated. In short, there is no scientifically sound proof that normalizing sugar has any positive effect on the pathophysiology of diabetic complications. And still, all antidiabetic medicine focuses primarily on reducing blood sugar. All these perfectly useless drugs have an annual turnover in hundreds of billions.

This means that the actual results of clinical trials have no bearing on practicing medicine. This has been demonstrated by not one but several examples. An entirely different set of principles operates in the drug market. Patients and doctors are equally gullible. There is no doubt that some medicines have been really effective and they have sound and robust science support. But for diseases where there is currently no real effective medicine, everyone is being fooled by the best of the bad drugs. If there is no real solution as of now, will you go for something that doesn’t work? Surprisingly the answer is ‘yes’ for most people. Rather than facing the reality that nothing works, people will try anything including witchcraft, magical, spiritual healing practices. We can’t blame them because many of the mainstream medicine practices are not different from witchcraft. They are there not because of their efficiency, proven in clinical trials. They are there because nothing else works, so why not try this? When there is no real cure, you still have to give something that doesn’t work.

And that actually works!! Not for curing any disease, but for the feeling of having done something, and of course for making money.

How peer reviews are degrading the spirit of science:

I have written many times about the problems in peer review systems. But most of this was from the author’s point of view. My experience from the other side is also quite rich. I have reviewed quite a few manuscripts for a variety of journals including some so called top ranking ones. This is not something I like to do, but it’s a part of researcher’s life, at least in the prevalent system.

A few months ago I received a manuscript for review. It was an interesting and quite off beat experiment. I liked the experimental design. The data and the analysis was all quite clean. But I thought the inferences that the authors had drawn were not quite logical. The results were being over-interpreted. The data only showed association but the authors confidently claimed a causal pathway without any further evidence. The results were specific to a given context but the inferences sounded as if a general law was being discovered. I wrote my comments accordingly saying that your experiments are ingenious but the interpretations need to be reconsidered. I also hinted that you don’t have to agree with my interpretation. If you think your interpretations are correct, you need to make them more convincing. A difference of opinion is not a sufficient ground to reject the manuscript, but kindly acknowledge in the paper that multiple interpretations are possible and reason out why you prefer one interpretation over the other.

The response of the authors was quite representative of a researchers’ behavior. Clearly they did not want to agree with my interpretation, which is fair. Having different opinion is a natural and desirable part of science. Open debates increase clarity, bring forwards many subtle aspects which would otherwise have remained hidden. But in a typical authors’ behavior with reviewers, they did not argue out their side. Instead, they pretended to agree with me, which obviously they did not. They did not want to change their original argument, but at the same time did not want to argue with the reviewer. So they rewrote the same inferences in a more round-about and ambiguous manner.  I was irritated. I would have welcomed a clear argument, even if it were different from mine. Respecting the authors’ right to differ with the reviewer, and the experiments themselves being interesting I did not recommend rejection. Finally the paper was published. Being in a high impact journal, was read widely and as I expected, came under some heavy criticism.

Attracting criticism is not necessarily a bad sign. It is a part of healthy science. The part that was clearly against the spirit of science is that the authors avoided committing blasphemy against the ‘reviewer God’. I know that this is not a stand-alone incident. This is the modal behavior of authors, the reason for it being very obvious. I have taken up an argument against the reviewers at times ending up in rejection. In a typical response, the reviewers and editors are not in a mood to argue further. You simple get a sweetly worded rejection. Any logical debate is impossible. Most authors are smart enough to avoid that. Some are even ready to change their entire argument for getting acceptance. This is business and getting published in a high impact journal is such a huge benefit than you can easily trade the quality of science to reap the benefit.

A number of times we see papers where the data actually contradict the main claim made in the conclusions. I had the opportunity to ask one of the authors of such papers and he told me that the ambiguous looking conclusions were actually rewritten after getting the reviewer’s comments.  There are two reasons for this trend. One is that a so called peer review is not really about a ‘peer’ relationship. It is more of a candidate and examiner relationship. An even better metaphor is that the editors and reviewers are God-men and the authors are worshipers. This makes practicing science one more religion where some are closer to the gods and others can access the gods only through them. The second reason is that the review remains confidential. So even if you make some logical somersaults there, it does not surface. What becomes public is a polished and painted argument covering up all logical cracks beneath it. The remedy for this is actually quite simple. Make all the reviews public, independent of acceptance or rejection. When everything becomes transparent, the arguments will have to become more logical. Differences of opinion will remain, but they will be open for the readers to judge. What can be better than this for the spirit of science? But do we really care for science?

Covid 19: A behavioural perspective

I wrote a number of posts and one research paper on the Covid 19 pandemic. I wrote about the epidemiological patterns, evolution of the virus and the need to change the strategy according to the changing context. Most of what I thought is coming out to be qualitatively true. Now there is genomic data showing a large number of mutations, signatures of positive selection on the mutations and the signs of reducing virulence. The fatality continues to come down. India today news on 1st Sept says that in a joint statement, experts of the Indian Public Health Association (IPHA), Indian Association of Preventive and Social Medicine (IAPSM), and Indian Association of Epidemiologists (IAE) advised the government to lift lockdown, reopen schools and colleges and not to rely too much on vaccines. In the month of May it looked like I was the only one saying this. Now there are “experts” saying the same.

But epidemiology and pubic health is not my core interest. My core interest is behavior. The pandemic was a unique and rare opportunity to observe different patterns of behavior. Human behavior invariably interacts with the virus. Behavioural patterns are shaped by the epidemic and behavior in turn shapes the course of the epidemic, even the biology of the virus. Optimizing one’s own perceived cost-benefits is an innate human tendency. Every player has a different cost benefit calculation. The perception of costs, risks and benefits are also shaped by different factors and that is a complex and interesting dynamics.

People perceive risks by what they see as well as by what they are told. There are many other examples where public health authorities have been warning people about various risks. Tobacco is a very good example. The statistical association between tobacco and cancer is consistently seen. There is enough awareness among people, warnings are prominently printed on every packet. But there are no signs of the market for tobacco going down in any form. The reason why people do not listen to the public health authorities is that there is a conflict between what they see and what they are told. People have their own intuitive sampling strategies and built in statistical algorithms by which they make their own inferences. Often they are different than the public health policies.

The health science literature projects odds ratios, risk ratios or hazard ratios to reflect the risk from a given factor like tobacco. These are essentially probability ratios of some kind. We conducted a small study of how people perceive risks, which is yet to be published but the results are extremely clear. We observe that people infer risks based on probability differences and not on probability ratios. We saw that even statisticians and public health personnel, who have been formally trained to use the ratio based indices, use probability difference when they have to make a behavioural decision for themselves in a game or imaginary context. The ratio based and difference based inferences can be diametrically opposite at times. If say among non-smokers the risk of cancer is one in thousand and in smokers one in hundred, smoking can be said to increase the probability of cancer ten-fold, but the actual increase in probability is only 0.009.  While the health authorities project the ratio, people’s intuitive sampling and statistical inference methods seem to have evolved to use the difference. The probability ratio is large but difference is small. So the risk of cancer fails to prevent smoking.

This applies to the risk perception for Covid-19 as well. Initially people did not have any opportunity to sample themselves. So they believed what they were told. As they started observing cases around them, a mental conflict started building up in their subconscious mind. They were told it’s a deadly virus but their subconscious sampling did not show that. What can be the effects of such a conflict? I feel it leads to an internal behavioural contradiction. While at a subconscious level the fear starts vanishing, at a verbal level they will still express fear. So in a questionnaire survey majority will agree that it’s a deadly virus and the pandemic is unprecedentedly dangerous. In reality, as soon as beaches, theatres and other public places are opened up they won’t mind crowding there. This has happened throughout the world, independent of the literacy, education, economic status of the society. This is because the risk of death by catching the infection, inferred by probability difference is very small and people calculate the risks by their own innate Bayesian algorithms. In India, with a population approaching 140 crore, living with a mean lifespan of 70 years, there are around 55,000 deaths expected every day. Covid deaths during the last two weeks appear to have stabilized at around 1000 per day. This means the death probability on a given day has increased from 0.0000393 to 0.00004. That is .0000007 per day or .00026 per year. Even if we make a limiting assumption that lockdown and masks make the probability of infection zero, the difference between following and not following preventive measures is too small to care. For a difference of this magnitude, people will not be willing to sacrifice their livelihood as well as pleasure activities. Therefore unless a lockdown in forcefully imposed, people are most unlikely to follow it. It is not ignorance, it is innate statistical calculations. “Creating awareness” will not work because people’s calculations directly contradict the preaching. However, more than the fear of infection or death, the social norm matters more. More people wear masks for the fear of punishment or to avoid strange looks by others than for the fear of infection. There is one more reason. For a large number of people the thought of getting admitted in an isolation ward, cut off from friends and relatives matters more than the fear of death.

In a cost benefit calculation, people innately differentiate between absolute and relative costs. For relative costs, if everyone is suffering to a similar extent, people don’t mind their own suffering. For absolute ones, others don’t matter. For example, for an addict, missing alcohol is an absolute cost. On the other hand, kids missing school is a big cost with long term consequences but it is perceived as a relative cost. My kid missing school is ok if all kids are missing it. So obviously there would be more pressure to start wine shops than starting schools. If parents are resisting reopening of schools for the fear of their kids getting infected, their resistance will persist as long as they can prevent reopening of schools entirely. But if other kids are attending, the cost of only their kid not attending becomes larger than the fear of infection. So if some schools start, all others will start with little resistance from parents.

Doctors and hospital staff, unlike common man, invariably have a biased sample. They see the serious cases disproportionately more frequently. So the risk in their perception will always be more than one in common man’s perception. Here again there will be a difference between a general practitioner and a Covid ICU ward intensivist, the latter having a much more biased sample.  So although a doctor’s knowledge needs to be respected, the statistical inference of common man is equally valuable because it is less biased.   

Health authorities and governments have a perceived ‘responsibility’ of people’s health. Under the pressure of such responsibility it is necessary to show that you have done something. Therefore they will prefer to do things that show up prominently. Whether the measures taken are really effective or not is a secondary concern. The primary concern is to minimize attracting criticism. This is a major force shaping the strategies of the health administration and government. A lockdown is a preferred response since it shows off more strikingly and is easier to implement than providing better patient care, inculcating clean habits in the society, taking better care of pollution, caring for of garbage handlers etc.

The vaccine and drug industry clearly has a commercial interest. They will always be bent on painting a fearful picture of the disease. They can do so successfully but only to a limited extent. They cannot stop people’s subconscious statistical inferences. As the perceived fear goes down inevitably, the market potential for vaccine will also go down. Nevertheless, people will go for a vaccine if it is free of cost or cheap enough and easily available. If it is costlier than the perceived fear, they won’t.

The behavioural basis of costly drugs with unproven or marginal benefits lies in the social norms of demonstrating that you did all you could to save your relatives. This is not to deny love. It certainly exists. But by the social norms, only loving your relatives is not enough. You need to demonstrate that to the society. Costly drug is one of the best ways to do that. The pharma industry knows this quite well and makes good business on it. People will be ready to spend huge amounts if one of their relatives or friends is under critical condition. Here the actual probability of saving the person does not count so much in the cost benefit calculation. To establish that you care more about someone than you care for money is important. If only the outcome mattered, then only the drugs with proven large benefits would have been in demand. But since the social display matters, the efficacy of the drug counts little. That’s why clinical trials of drugs often show contradictory or marginal benefits, but all drugs are sold at a very high price.

The research community has its own interests too. A pandemic is a good opportunity to get quick publications, make headlines and seek more research grants. Therefore this community will be more interested in spreading terror. It has been repeatedly seen that whenever someone made a more realistic statement, he or she was immediately and heavily criticized. There is a very clear declining trend in the death rate globally. But researchers have rarely ever talked about it. Saying that the virus is not as deadly as perceived earlier is politically incorrect and it would be rare for a researcher to say so. When data show a declining death rate, they will not analyze or reason it out. They will simply ignore it. The best example is that of Sweden. Sweden took a different path and did not impose a lockdown. Initially the death toll was high. There were heated debates on whether Sweden took a suicidal path. But today Sweden’s death rate has declined by an order of magnitude even without a lockdown, so it is natural that nobody talks about it.

So far I have tried to predict what the expected behavior of different players is, with no value judgment. I am not saying someone is right or wrong. This is what baseline selfish behavioural motives will be. Conscious decisions overriding the innate tendencies are not impossible. But you don’t expect everyone’s virtue to be the same. So modal behavior is most likely to follow what I described. There can always be glorious exceptions.

However, as a student of science, there is one issue where I would like to bring in the ‘right-wrong’ judgment. People believe in science and scientists to a large extent. This trust is valuable and needs to be maintained. So I would urge scientists not to play ostrich and openly admit the obvious trends in the data and change the strategic advice accordingly. We have seen during the pandemic that so often irresponsible statements were made and retracted. Having different views is a good sign. Looking for evidence for or against a viewpoint is also fine. But we have seen that statements were often retracted under conformity or political pressure. For science, only sound theory, models and evidence matters. At times, being wrong is not a crime, but if and when evidence shows that you are wrong, admitting and correcting oneself is necessary. If this is not done, people will lose faith in science and in scientists. This is particularly important for the fact that mainstream health organizations have largely kept mum on the declining fatality rate. O many people have lost their livelihood because of the fear of the virus. If they know eventually that the fear was overblown and scientists never admitted that, they would lose trust in science. If people lose trust in science or in scientists, what can be a bigger social tragedy? What will be the future course if people continue along their innate behaviours? Biologically, the virus will go on becoming milder, but will not be eradicated for quite some time. It will stay in the population more peacefully for at least a few more years, being just another virus. But even if it remains at its current virulence, gradually the seriousness of the disease in people’s perception will vanish. Health authorities may not admit this clearly but they will talk about the seriousness of the disease less and less frequently and ultimately stop talking about it. In the news channels and media, the news value will keep on diminishing until nothing is perceived as worth reporting. There are talks about fundamental and permanent changes brought about by the pandemic, but that is less likely. A few practices might become irrelevant rituals and persist for the name sake. Ultimately most good and bad things are most likely to return to the baseline, as if nothing had happened.

Covid in India: Why the strategies need to change

Let’s us do some simple maths. Readers who dislike maths can jump straightaway to the section “What does the math tell us?” Here you can grasps the inferences by common sense logic. Doing maths of course needs a set of assumptions. The assumption here is that the infection is a probabilistic process, a fair, logical and often used assumption. The control strategy followed so far is that whenever an infectious individual is found, he/she is quarantined. The contacts are traced as much as possible, tested and quarantined if positive. This practice can reduce the probability of spreading the infection from this infectious unit. For every infectious unit found, you follow the same procedure. There is some probability that some virus leaks out from the quarantine room, some contact remains untraced and so the infection spreads.

Let p be the probability that you successfully prevent spread from this unit. There are n number of such units so the probability that you successfully prevent spread from all the units is pn. If you achieve this, the epidemic ends there. If you don’t, the virus escaping from the n.(1-p) units creates X new units each. So the most probable number of new units created is n.(1-p).X. If this is less then n, the epidemic slowly vanishes, if greater then n, it spreads.

So far it is simple. But there is one more twist to this. You have a system that would do the contact tracing. The system has a finite capacity. So if n is very large, the efficiency of contact tracing suffers a little bit. If the epidemic is spreading, n increases exponentially whereas the system may grow at the most linearly. So the contact tracing efficiency will almost inevitable diminish as n increases. As a result p is not independent of n. But we will make p fairly robust to changes in n by using an equation p = k/(k+n) where k is an index of the efficiency of the system. If you want to slow down further the effect of n on p, a little more fancy equation p = km/(km+nm) can be written where greater the power, slower is the decrease in p with n but to suddenly drop when n is close to k. With this form the intuitive meaning of k is how many number of cases the system can handle without much loss of contact tracing efficiency. If k is large, a substantial increase in n is tolerated without proportionate reduction in the efficiency of contact tracing. But at very large n the efficiency per infectious unit suffers thereby decreasing p. I simulated with a starting n at t=0 and a set of assumed X and k to calculate p and accordingly what will be the expected new n  at t+1. The new n changes p again in the next time unit and so on.

One can increase k by imposing strict quarantine added by general lockdown and other restrictions so as to keep p high. So when and with what probability can I drive the virus to extinction by these measures?

Simulations show that the success works with a threshold phenomenon. At a given k, you can arrest the infection effectively and drive the virus to extinction up to a threshold value of n. If the starting n is higher than the threshold, arresting the infection becomes impossible. You may still stop the infection by increasing k, that is trying to make the restrictions more and more rigid. But the required increase is not linear, for a desired increase in threshold n, K has to increase in a power relation. At m=1 it increases in square proportion, the power being smaller at higher m.

What does the maths tell us?

So whether one can successfully drive a virus to extinction depends upon the parameters X, i.e. if a virus leaks from an infectious unit, how many new units it can create; k, the efficiency of quarantine and contact tracing and thirdly the starting n, the number of infected. The two most important inferences of the maths are (i) there is a threshold n above which control of the epidemic by quarantine and lockdown becomes impossible at any given context. (ii)  this threshold n  can be increased by increasing the strictness of quarantine and lockdown measures, but for which the efficiency needs to increase in square or some such power of n.

Now even if we admit that the first lockdown in India was not very efficiently executed for whatever reasons, we can’t say a more efficient lockdown will work better because now if the n has increased by 1000 fold, the efficiency will have to increase several thousand or a million fold to drive the virus to extinction.

Forget about the actual parameter values. It is necessary to appreciate at least qualitatively that the efficiency of lockdown required to drive the virus to extinction increases disproportionately more than the target n. In India, owing to high population density, X is expected to be high. If the first lockdown did not drive the virus away even at a lower n, now at several orders of magnitude higher n, it is impossible to stop the transmission. So the focus needs to shift from stopping the spread in the general population to specific care of the high risk group at both preventive and treatment level. Fortunately for us, the death rate has been coming down consistently and rapidly. Better medical facilities and better patient care can bring it down further. Disinvesting from strategies that are not going to work will allow us to invest more in the more promising strategies.

कोव्हिड: आकडे आणि धोरणं

कोव्हिडचे आकडे काय बोलताहेत हे आपण मागल्या लेखात पाहिलं. पण आकड्यांचं हे बोलणं न ऐकताच अनेक धोरणं आखली आणि राबवली गेली आहेत. ही गोष्ट भारतापुरती मर्यादित नाही हे आवर्जून सांगितलं पाहिजे. सगळ्या जगातच आकड्यांचा अडाणीपणा भरपूर प्रत्ययाला आला आहे. आपण इथे विचार मात्र जास्ती करून भारताचाच करणं नैसर्गिक आहे. कोव्हिडचं स्वरुप सुरुवातीला वाटलं होतं त्यापेक्षा खूपच कमी घातक आहे आणि दिवसेंदिवस त्याची घातकता आणखी आणखी कमी होत आहे याची आकडेवारी आता सर्वांसाठी खुली आहे. जर रोग भयंकर असला तर उपाय त्रासदायक असला तरी करावा लागतो. प्रत्यक्षात तो वाटलं त्यापेक्षा एक दशांशानेच घातक आहे. त्यामुळे आता या रोगाविषयीची आपली धोरणं बदलायला हवीत. लॉकडाउनचा उपाय हा पोटावर बसलेल्या माशीला तलवारीने मारण्यासारखा आहे. जोवर कँसरला आळा घालण्यासाठी तम्बाखू आणि सिगरेटबंदी होत नाही तोवर सरकारनी कोव्हिडला आळा घालण्याच्या उदात्त हेतूनी पुनश्च लॉकडाउन केलं यावर कुणी दूधखुळाही विश्वास ठेवणार नाही.

आकड्यांना विज्ञानात महत्त्व असलं तरी सगळ्याच गोष्टी आकड्यांमधे पकडता येत नाहीत. विज्ञानात कुठलीही गोष्ट वस्तुनिष्ठ पद्धतीनी दाखवता आणि मोजता येण्याला फार महत्त्व आहे. पण प्रत्यक्षात महत्त्वाच्या असलेल्या सगळ्याच गोष्टी मोजता येण्यासारख्या नसतात. खरोखर महत्त्वाच्या असलेल्या गोष्टी मोजता येत नसतील तर ज्या गोष्टी मोजता येतात त्यांना महत्त्वाचं मानायचं असा एक मोह वैज्ञानिकांना होतो. त्यामुळे काही काही गोष्टी महत्त्वाच्या असूनही त्याविषयी गरजेपेक्षा कमी बोललं जातं. अशी एक महत्त्वाची गोष्ट म्हणजे उपचार करणा-या डॉक्टरांचा अनुभव. किती चाचण्या झाल्या आणि किती पॉजिटिव आल्या एवढच बोलून चालणार नाही तर प्रत्यक्ष त्यावर काम करणा-यांना काय दिसत आहे त्याचीही दखल घ्यायला हवी. कोव्हिडच्या साथीमधे लक्षणे न दाखवणा-यांचं प्रमाण नव्वद टक्क्यांपेक्षा अधिक असल्याचे अनेक अभ्यास सुचवतात. हे प्रमाण आणखी वाढेल असं सुचवणारीही काही लक्षणं दिसताहेत. तेंव्हा टेस्ट पॉजिटिव येते का नाही, किती जणांच्या पॉजिटिव आल्या या आकडेवारीला यापुढे फार महत्त्व राहणार नाही. देण्याची आवश्यकताही नाही. सर्दी कोणाला होते याची आपण राष्ट्रीय पातळीवर नोंद ठेवतो का? जर ९५% लोकांसाठी कोव्हिड सर्दीसारखाच असेल तर त्या प्रत्येकाची चिंता का करायची? सर्दीपेक्षा कोव्हिड खूपच जास्ती घातक आहे पण तो फक्त काही टक्के लोकांना. त्यामुळे पॉजिटिव किती आले यापेक्षा नक्की धोकादायक लक्षणं कोणती? ती लवकर कशी ओळखायची? रुग्णालयात दाखल करणं कधी अत्यावश्यक आहे? कधी घरीच काळजी घेऊन चालेल? या गोष्टींवर अनुभवी डॉक्टरांनी अधिक संशोधन, चर्चा आणि प्रबोधन करणं आवश्यक आहे. ज्याला दाखल करण्याची आवश्यकता आहे अशा कुठल्याही कानाकोप-यातील व्यक्तीला सुद्धा काही मिनिटांमधे अॅम्बुलेंस मिळेल की नाही? कुठे दाखल व्हायचं? कसं व्हायचं हे समाजातल्या प्रत्येकाला नीट माहिती आहे की नाही? यावर सगळा फोकस असायला हवा. संसर्ग होणा-यांपैकी अगदी कमी टक्क्यांवर घातक परिणाम दिसतात. ही टक्केवारी दिवसेंदिवस घटतही आहे. पण जोवर ती आहे तोवर अशा रुग्णांची जास्तीत जास्त काळजी घेण्यावर आणि त्याना वाचवण्यावर भर दिला पाहिजे. जर त्यांच्यातला मृत्युदर खाली आणण्यात आपण नेत्रदीपक यश मिळवू शकलो तर बाकी लोकांत विषाणू हवा तितका बागडेना का!!

आपल्या डोळ्यासमोर कॉलरा, गॅस्ट्रोसारखी उदाहरणं आहेत. एकेकाळी यांनी माणसं, विशेषतः लहान मुलं पटापट मरत होती. या रोगांचा नायनाट मुळीच झालेला नाही. याच्या जंतूंचा संसर्ग होणं मुळीच थांबलेलं नाही. पण आता मृत्यूदर एकदम कमी झाला आहे कारण याची लक्षणं दिसली तर लगेच काय करावं याविषयी योग्य प्रबोधन झालं आहे. आणि ते देशाच्या कानाकोप-यातल्या आरोग्यसेवकांपर्यंत अगदी व्यवस्थित पोचलं आहे. म्हणजे सर्वर्थानी नाही पण उपयुक्त अर्थानी आपण कॉलरा, गॅस्ट्रोची लढाई जिंकली आहे.

कोव्हिड पसरण्याचा वेग पाहता आपल्याला संसर्ग थांबवता येईल अशी शक्यता आता दिसत नाही. पहिल्या लॅाकडाउनच्या काळात तो प्रयोग करून झाला. त्यानी काही काळ संसर्गाचा दर कदाचित कमी झाला असेल कदाचित. तो झाला असं दाखवणारा पुरावा नाही. झाला अशी आपण श्रद्धा ठेऊ हवं तर. पण व्हायरसचा निःपात करणं साधलं नाही हे नक्की. हा कुणाचा दोष नाही. भारतासारख्या गर्दी, गर्दी आणि गर्दीच्या देशात हे मुळात अवघडच होतं. पण तो ही प्रयत्न आपण करून पाहिला. आणि काही नाठाळ वगळता बहुतेक लोकांनी त्याला मनापासून साथही दिली. आता रोगाची साथ त्यापलीकडे गेली आहे. तेंव्हा संसर्ग थांबवण्यापेक्षा मृत्युदर आणखी कमी करण्यावर सर्व लक्ष केंद्रित केलं पाहिजे. एकीकडे हे प्रयत्न चालू आहेतच. पण दुसरीकडे आज किती पॉजिटिव निघाले त्याचे आकडे दाखवून लोकांना निष्कारण घाबरवलं जात आहे. आता लोकांनीच आकड्यांचे अर्थ नीट ओळखून त्याला महत्त्व द्यायचं आणि निष्कारण घाबरायचं बंद केलं पाहिजे. प्रत्यक्षात कुठलीही लक्षणं न दाखवता पॉजिटिव निघणा-यांचं प्रमाण वाढत आहे हे चांगलंच लक्षण आहे. वाईट नाही. कारण असे लोकच समाजाला हर्ड इम्युनिटीकडे अधिक लवकर पोचवतील. क्वचित केंव्हातरी अशा लोकांकडून एखाद्या वृद्ध व्यक्तीला संसर्ग होऊ शकतो हे अशक्य नाही. पण आज तरी अशा संसर्गाचं प्रमाण फार असल्याचं दिसत नाही. तसं असतं तर एव्हाना मृत्यूनी देशभर थैमान घातलं असतं. प्रत्यक्षात भारतात दररोज २५००० च्या वर मृत्यू होतात. त्यावर दिवसाला ५०० कोव्हिडचे. म्हणजे कोव्हिडनी सुमारे २ % नी देशातला मृत्युदर वाढवला आहे. हे घाबरून जाण्यासारखं नक्कीच नाही. अर्थात हे दोन टक्के सुद्धा कमी करण्याचं ध्येय आपण ठेवलं पाहिजे पण त्यासाठी आख्ख्या समाजाला ओलीस ठेवणं समजण्या सारखं नाही.

थोडक्यात संसर्ग वेगानी वाढणं ही चिंता करण्याची गोष्ट नाही. चिंता करण्याची गोष्ट ही की समाजातील ज्या व्यक्तींना कोव्हिड घातक ठरण्याची शक्यता आहे अशा वृद्ध, मधुमेही, हृदयरोगी व्यक्तींची काळजी कशी घ्यायची. म्हणजे आता आपली धोरणं साथ पसरण्याला आळा घालण्यापेक्षा जास्ती धोका असलेल्या व्यक्तींची काळजी घेण्याकडे वळली पाहिजेत.

बदललेल्या धोरणातलं पहिलं म्हणजे लॅाकडाउन ची आता कुठेच आवश्यकता नाही आणि त्याचा उपयोग होतो असा पुरावाही नाही. आता सर्व लोकांना आपला रोजगार परत मिळण्याचा मार्ग मोकळा झाला पाहिजे. क्वारंटाइन ही गोष्ट लॅाकडाउन पेक्षा वेगळी आहे. त्याची आवश्यकता नक्कीच आहे आणि अजून काही काळ राहील. पण आता कोव्हिड पॉजिटिव लोकांची संख्या एवढी वाढली आहे की प्रत्येकाला क्वारंटाइन फॅसिलिटी देणं शक्य नाही. होम क्वारंटाइनची पद्धत सुरु झाली आहेच. पण यामधे लक्षणांवर बारकाईनी लक्ष ठेवण्यावर, त्यासाठी पुरेसं प्रबोधन करण्यावर भर दिला गेला पाहिजे. एखादी व्यक्ती पॉजिटिव निघते तेंव्हा तिला जर लक्षणे नसतील तर काही व्यक्तींना ती कधीच दिसणार नाहीत, काहींना थोडया दिवसात दिसू लागतील, त्यापैकी काहींमधेच ती गंभीर होतील. तेंव्हा गंभीर केस लवकर कशी ओळखायची आणि तिला योग्य ते साहाय्य लगेच कसं उपलब्ध करून द्यायचं हा नजीकच्या भविष्यातला कळीचा मुद्दा असणार आहे. गंभीर केसला एकीकडे चांगले उपचार आणि दुसरीकडे काटेकोर क्वारंटाइन अशा दोन्ही गोष्टींची आवश्यकता आहे.

एखादी केस बिन लक्षणाची आणि एखादी गंभीर होण्यामागे दोन कारणं असू शकतात. एक तर व्यक्तीव्यक्तींच्या प्रतिकारक्षमतेतला फरक आणि दुसरं म्हणजे विषाणूमधलाच फरक. विषाणूंमधे सतत म्युटेशन, सतत बदल होत असतात. त्यामुळे त्यांची घातकताही कमी अधिक होत असते. एका बिन-लक्षणी व्यक्तीमधे या दोनापैकी कोणतं कारण काम करत आहे हे सांगता येत नाही. पण समाजातल्या काहींमधे हे तर काहींमधे ते कारण असणार हे तर्काला धरून आहे. आता आपण सर्व गंभीर केसेसना काटेकोरपणे क्वारंटाइन करत राहिलो आणि बिन-लक्षणी केसेस मधून विषाणू अधिक पसरत राहिला तर कमी घातक विषाणूचा अधिक प्रसार होईल असे उत्क्रांतीचे गणित सांगते. आणि गेल्या तीन महिन्यात सातत्याने कमी होणारा मृत्युदर या गणिताला पुष्टीही देतो.  त्यामुळे गंभीर केसेसना काटेकोरपणे क्वारंटाइन करत राहिलो तर विषाणूची घातकता दिवसेंदिवस कमी होत जाईल. सर्व केसेसना क्वारंटाइन करण्याचा कितीही प्रयत्न केला तरी नजीकच्या भविष्यात ते व्यवहार्य राहणार नाही. पण हा चिंतेचा विषय मुळीच नाही. किंबहुना बिनलक्षणी व्यक्तींनी खुशाल लोकांमधे मिसळणं दीर्घकालीन फायद्याचंच ठरेल अशी शक्यता आहे. खुशाल खेळायला हरकत नाही असा हा जुगार आहे कारण झाला तर फायदाच, आणि तो न खेळण्याचा पर्याय आपल्या हातात राहण्याची शक्यता एवितेवी दिसतच नाही. मग तो न खेळण्याचं नाटक तरी का करायचं?

असं व्यवहार्य तत्त्वज्ञान स्वीकारलं तर अनेक गोष्टी पूर्ववत होतील आणि तशा होण्यातच समाजाचं हित आहे. आता शिक्षण बंद ठेवण्याचं बदललेल्या परिस्थितीत काहीच प्रयोजन दिसत नाही. तरुण वयात कोव्हिडचा संसर्ग झाला तरी गंभीर लक्षणं दिसण्याचं प्रमाण मुळातच कमी आहे. आणि शिक्षण ही दारूच्या दुकानांपेक्षा अधिक महत्त्वाची गोष्ट नक्कीच आहे. त्यामुळे किमान महाविद्यालये आणि माध्यमिक शाळा पूर्ववत न करण्याचं काही तर्कशुद्ध कारण दिसत नाही.

आता लॅाकडाउन आणि कंटेनमेंट ची अंमलबजावणी करण्यात वेळ आणि पैसा वाया घालवण्यापेक्षा लोकांना स्वछ्तेच्या सवयी लावण्यावर भर द्यायला हवा. रस्त्यात थुंकणे आणि तत्सम अस्वच्छ सवयींना दंड करण्याचं प्रमाण वाढायला हवं. कोट्यावधि लोकांना थोडया तरी स्वच्छतेच्या सवयी लागल्या तर काही हजार लोकांचं बलिदान वाया गेलं नाही असं नक्की म्हणता येईल. कोव्हिडवर प्रभावी लस या वर्षात तरी येण्याची शक्यता नाही. विषाणूचा नायनाट करणे दाट लोकवस्तीच्या देशात शक्य नाही. हर्ड इम्युनिटी सव्वाशे कोटींच्या लोकसंख्येला यायला हवी असेल तर दोन पाच वर्षे तरी लागतील किंवा आपणहोऊन प्रयत्नपूर्वक संसर्गाचा वेग वाढवावा तरी लागेल. म्हणजे हे तीन्ही उपाय साधणारे नाहीत. आता आपण या विषाणूला स्वीकारणे, त्याच्या सकट पुन्हा जोमाने कामाला लागणे आणि अधून मधून गंभीर निघू शकणा-या आजा-यांची शक्य तितकी काळजी घेणे हाच सर्वात चांगला उपाय आहे. दाट शक्यता अशी आहे की काही काळातच इतर सर्दी, खोकला, तापासारखाच हा एक होऊन जाईल.

कोव्हिड: आकड्यांचे अर्थ

जॉन अॅलन पावलॅास या लेखकानी १९८८ साली Innumeracy नावाचं एक पुस्तक लिहिलं. Innumeracy हा शब्द तो illiteracy ला समांतर शब्द म्हणून वापरतो. त्याचं म्हणणं असं की सामान्य माणूस शिकून साक्षर पटकन होतो, म्हणजे त्याला अक्षरं, शब्द आणि त्यांचे अर्थ चांगले समजतात. पण आकडे वाचता आले तरी आकड्यांचे अर्थ मात्र बहुतेकांना समजत नाहीत. आज कोव्हिडच्या साथीच्या संदर्भात पावलॅासच्या म्हणण्याचा पावलोपावली प्रत्यय येतो आहे. सर्व प्रकारच्या माध्यमातून आकडे नुसते फेकले जात आहेत आणि त्याचे अर्थ न कळल्यामुळेच सामान्य माणूस गोंधळलेला आणि धास्तावलेला आहे.

वास्तविक मोजमाप आणि आकडे विज्ञानात खूप महत्त्वाचे असतात. पण आकडेवारी हे दुधारी शस्त्र आहे. समजले तर फारच उपयुक्त, नाही समजले तर गोंधळ वाढवणारेच फक्त नाहीत तर पूर्णपणे चुकीच्या मार्गाला लावणारे सुद्धा. वास्तविक आकडे समजण्यासाठी जे ज्ञान लागतं ते आपण शाळेतच शिकतो. त्यापेक्षा फार जास्ती गणित शिकण्याची गरज नसते. आकड्यांना काही सांगायचं असतं आणि ते आपण खुल्या मनानी ऐकलं तर सहज ऐकू येतं. पण हे खुलं मन दुर्मिळ आहे. आकडेवारी वापरणा-या बहुतेकांनी आकडे पाहण्याच्या आधीच स्वतःचं मत बनवलेलं असतं किंवा कुठला निष्कर्ष काढला असता स्वतःचा फायदा आहे ते आधीच ठरवलेलं असतं. आणि मग आकड्यांना स्वतःला काय सांगायचय ते न ऐकता आपल्या जे सांगायचय ते आकड्यांमार्फत कसं वदवता येईल असं ते पाहत असतात. कोव्हिडच्या साथीचे आकडे स्वतः काय म्हणताहेत ते पाहूया. साथीच्या रोगाच्या प्रसाराचं गणित चक्रवाढ व्याजाच्या गणितासारखं असतं. आज नव्यानी संसर्ग झालेली माणसं संसर्ग पसरविणा-यांच्या मुद्दलात मिळवली जातात आणि संसर्ग आणखी पसरतो. मात्र मेल्यामुळे किंवा बरे झाल्यामुळे या मुद्दलात दुसरीकडे घटही होत असते. जर नव्यानी संसर्ग होणा-यांचं प्रमाण घट होणा-यांच्या प्रमाणापेक्षा जास्ती असेल तरच साथ पसरते. पण जेंव्हा पसरते तेंव्हा दिवसेंदिवस रोग्यांची संख्या चक्रवाढीने वाढतच असते. आपण जेंव्हा काही प्रतिबंधात्मक उपाय वापरतो, तेंव्हा या चक्रवाढीच्या गणितातला व्याजाचा दर कमी होतो. म्हणजे रुग्णांचा आकडा वाढण्याचा दर कमी होतो. आकडा तरीही वाढत राहू शकतोच. मग आपण योजलेल्या प्रतिबंधात्मक उपायांचा काही उपयोग झाला की नाही हे आपण रोग पसरण्याचा दर कमी झाला की नाही यावरून ओळखायचं, रुग्णांच्या संख्येवरून नाही. मार्चच्या मध्यापासून ते मेअखेरपर्यंत आपण लॅाकडाउन पाळला आणि एक जून पासून बंधनं उठवायला सुरुवात केली. बंधनं उठवल्यावर रोग पुन्हा अधिक वेगाने पसरू लागला का? तर भारतामधल्या, महाराष्ट्रामधल्या आणि पुण्यामधल्या या आलेखांकडे पाहा. दररोज किती नवे करोना पॉझिटिव सापडले त्याची पाच पाच दिवसांची धावती सरासरी यात तारखेनुसार दिली आहे. फक्त त्यासाठी घातांक गणित किंवा लॅागॅरिदम वापरलं आहे. त्यामुळे ही सरासरीची आळी ज्या चढावानी वर चढते तो चढाव रोग पसरण्याचा दर दाखवतो.

आपल्याला असं दिसेल की लॅाकडाउन उठल्यानंतर हा चढाव वाढलेला तर नाहीच, उलट भारताच्या आणि महाराष्ट्राच्या आलेखात तो कमीच झाला आहे, तर पुण्याच्या आलेखात तो थोडा कमी होऊन परत पहिल्याइतका झाला आहे. म्हणजे लॅाकडाउन उठल्यावर रोग अधिक वेगाने पसरू लागला म्हणून आता रुग्णांचे आकडे वाढताहेत हे म्हणणं एकतर आकडे न समजण्याचं लक्षण आहे किंवा जाणीवपूर्वक दिशाभूल करण्याचा प्रयत्न आहे. अर्थातच परत लॅाकडाउन लादण्याची भाषाही तितकीच तर्कदुष्ट आहे हे सांगायला नकोच.

पण दुसरीकडे प्रत्यक्ष रुग्णांची संख्या वाढते आहे आणि त्यामुळे वैद्यकीय सेवांवर ताण येतो आहे ही समस्याही खरीच आहे. या प्रश्नाच्या संदर्भात साथीच्या संसर्गाचा दर महत्त्वाचा नसून प्रत्यक्ष रुग्णसंख्या महत्त्वाची आहे. पण पुन्हा लॅाकडाउन लादण्यानी हा प्रश्न सुटूच शकत नाही. संसर्गाचा दर मारे कमी झाला तरी ही संख्या वाढणारच, आज ना उद्या रुग्णालये कमी पडणारच. साथीच्या सुरुवातीला लॅाकडाउन आणण्याचा हेतू हा होता की एकदम मोठी साथ झेलायला आपल्या वैद्यकीय व्यवस्थेची तयारी नव्हती. ती करायला काही अवधी मिळायला हवा होता. लॅाकडाउन फार काळ चालणं परवडण्यासारखंच नाही कारण लोकांच्या पोटापाण्याचा प्रश्न आहे. साथीच्या सुरुवातीपासून साथ काय वेगाने पसरू शकेल याची गणिते मांडली जात होती आणि ती प्रसिद्धही होत होती. या गणितांची दखल घेऊन वैद्यकीय सुविधा किती वाढवाव्या लागणार आहेत ते ठरवून नियोजन करता आलं असतं. प्रत्यक्षात या गणितांच्या हो-यापेक्षा कितीतरी कमी दरानी संसर्ग वाढला आहे. आणि तरीही आता वैद्यकीय सुविधा अपु-या पडत असतील तर प्रशासनाला गणित समजत नाही याचंच ते द्योतक आहे. पण परिस्थिती इतकी वाईट नाही हे सुद्धा आपल्याला आकडेच सांगताहेत. सर्व जगात कोव्हिडमुळे होणा-या मृत्यूचं प्रमाण सातत्यानी कमी होत आहे. अनेक देशांत मार्च आणि एप्रिलच्या सुरुवातीला संसर्ग झालेल्यांपैकी पाच, दहा किंवा अधिक टक्क्यांनी लोक मरत होते. काही देशात १७ % मृत्यू सुद्धा नोंदले गेले आहेत. पण एप्रिल मध्यापासून सगळीकडेच मृत्युदर कमी कमी होत गेल्याचं दिसून आलं आहे. ते मान आता दोन टक्क्यांवर आलं आहे. भारतात हा दर चार टक्क्यांच्या वर कधीच गेला नाही पण तोही आता दोनच्या खाली आला आहे. संसर्ग झालेल्या प्रत्येक व्यक्तीची चाचणी होत नाही. जर लक्षणे दिसू लागली तर चाचणी करून घेण्याची शक्यता खूपच वाढते. त्यामुळे संसर्ग झालेल्या पण चाचणी न झालेल्या बहुतेक व्यक्ती लक्षणं न दाखवणा-या असतात. हे सर्वच देशांमधे कमी अधिक प्रमाणात खरं आहे. याचा हिशेब विचारात घेऊन काळजीपूर्वक मृत्यूदर काढणारे अभ्यासही आता प्रसिद्ध झाले आहेत. नेचर सप्ताहिकातल्या एका शोधनिबंधाने अशा अनेक अभ्यासांना एकत्र करून प्रत्यक्षात मृत्युदर ०.५ ते १ % एवढाच आहे असा निष्कर्ष काढला होता. भारतात चाचणी न झालेले कोव्हिड पॉजिटिव किती असतील हे नक्की सांगता येत नाही. पण त्यांचा समावेश केला तर भारतातला मृत्युदर ०.५ % हूनही बराच कमी निघू शकतो.

म्हणजे कोव्हिडची घातकता आधी वाटलं होतं त्याच्या एक दशांश एवढीच आहे. म्हणजे फार काळजी करण्याचं कारण नाही. मात्र काळजी घेण्यात हयगय करावी असा याचा अर्थ नाही. आधी वाटलं त्यापेक्षा कमी घातक असला तरी हा दुर्लक्ष करण्याचा विषय नाही. वैद्यकशास्त्राचं एक तत्त्व असं आहे की प्रत्येक रोगाचा मुकाबला केलाच पाहिजे. मग रोगी चार असोत वा चार हजार, तरूण असोत वा वृद्ध, गरीब असोत वा श्रीमंत. पण आपण आकड्यांचे खरे अर्थ ओळखत असलो तर त्याप्रमाणे धोरणं बदलायला हवीत. घरात बिबट्या घुसला तर करण्याचे उपाय वेगळे असतात आणि ढेकूण झाले तर करण्याचे वेगळे असतात एवढा तरी विवेक असायलाच हवा.

Covid: Anyone here understands numbers?

This question was triggered by the announcement of a lockdown again in Pune city. The lockdown decision must be based on a set of assumption, which I think are the following

1. During the earlier lockdown the rate of spread of the infection was under “control”, by whatever it means.

2. After the partial lifting of the restrictions on 1st of June, the rate of spread increased.

3. The facilities for accommodating patients in need of hospitalization and critical care are saturating. We can no more accommodate more patients.

4. Another lockdown will reduce the number of patients. Now let us see the actual numbers. Plotted below is the time trend in 5 day running average of daily reported cases on a log scale. So far the number of positives is such a tiny fraction of the total population, that the number of susceptibles is not a limiting factor in the dynamics. So the slope of the log transformed data is straightaway an indication of the rate of spread of the infection. It can be seen easily with the Indian data, Maharashtra data as well as Pune data that just before the lockdown was lifted, the slope had started declining due to some reason. In India as well as in Maharashtra the slope remained lower whereas in Pune the slope increased again to match the earlier slope. In no case the slope increased. This means that there is NO evidence at any scale that the rate of transmission increased after lifting the restrictions. So saying that the infection is spreading more rapidly after relaxing the restrictions is either an indication of not understanding numbers, or some deliberate motive to propagate lies.

In support of the theory that the infection is spreading faster after lifting the lockdown, they give the absolute number of patients which is on the rise. But the absolute numbers would have gone up even with the lockdown. Absolute numbers say nothing about the rate of spread. They are bound to go up even with the rates that were present during the lockdown.

I will be surprised if the politicians and administrators do not understand statistics. But I believe there are people from science and medicine advising them. At least they are expected to understand numbers. I know in Pune city there is a group of scientists, advising PMC. I had an impression that at least they understand science. But may be, I have to change my opinion now.

The cause of worry is said to be the increasing number of patients saturating the available beds. Clearly here the absolute number of patients matter, not the rate of spread. But will a lockdown reduce the numbers? Currently there is no evidence that lockdown reduces the rate of transmission. Earlier lockdown experience indicates that it certainly does not result into a negative trend in numbers. But even if we assume that it will reduce the slope, it still cannot bring down the absolute numbers. They will still be growing may be at a slightly reduced rate. At the best, instead of saturating today, the beds will be saturated after 3-4 days. So lockdown is not at all a solution to the saturation problem.

One of the important expected outcomes of the first lockdowns was that we did not have enough facility to handle a large number of patients in the beginning. The breathing period that the first lockdown gave was meant to boost up our infrastructure, create more wards for Covid patients. Many cities in the world did this quite efficiently but did Pune do it? Very early in the pandemic, there were dozens of mathematical models predicting the possible numbers that hospitals may have to accommodate in the coming months. The actual spread of the infection has been much slower than what most models predicted. And even then if we are running short of beds now, it simply reflects on the inability of the administration and their scientific advisers to read numbers. John Allen Paulos wrote a book in 1988 called “Innumeracy”. He uses the word with a meaning parallel to illiteracy. Educated people learn to read, write and understand letters, words and their meanings. But most people don’t seem to understand numbers. They may at the most be able to read and write them. Understanding numbers is a different ball game. This is ok for laymen. But I wonder, is there nobody in Pune who really understands numbers and so can come out and say, NO! Lockdown is not the solution! It is not going to work, because the problem a lockdown can potentially solve, simply does not exist. The rate of spread of the epidemic has not increased by lifting lockdown, so it is not going to come down by imposing it again.