Problems with the Indian supermodel for COVID-19

Basing public health policy on flawed models can be dangerous

Puzzling fact: It makes little sense to have 24 parameters, all changing, in a model.

We predict the future by extrapolating from the present, based on what we’ve learnt from the past. To estimate how many cases of COVID-19 will be seen in India two months from now, we must have an idea of the number of people who are currently infected. For this, we must know the trajectory of the disease in the past as well as understand how infected people spread the disease to those as yet uninfected. Mathematical models describe this understanding in terms of equations, using input from epidemiologists. These can be used to make predictions for the future.

Some months ago, the Indian government’s top science agency, Department of Science and Technology (DST), decided that it would support the development of a single “supermodel” for COVID-19 in India. This would combine the best features of models from India and worldwide. A high-level committee was set up to do this, composed of eminent scientists, including several epidemiologists. The report of the committee, in the form of a presentation of the National Supermodel Committee and a paper that was fast-tracked in the Indian Journal of Medical Research, are now available.

Let’s divide the report into two broad parts. The first part contains general recommendations for India. The eminence of the panel adds weight to them. It warns that the gains of the past several months can be dissipated if distancing measures are reduced in the upcoming festival season. It stresses that continued attention to masking is critical. It suggests that, provided we pay attention to these, India may hope to enter the new year without seeing any further sustained increase in the number of cases. All these points are almost certainly valid. All the members of the supermodel committee have signed on to this part of the report.

The second is the work described in the published paper about the supermodel. Only three members of the committee are authors of this paper. The authors are an eminent computer scientist, an applied mathematician famous for work in control theory and a distinguished ex-army officer with a medical background. All are well known names. None are epidemiologists, even though the committee as a whole possessed this expertise.

First, the supermodel assumes something unusual. All generally accepted models for COVID-19 so far assume that everyone is equally susceptible to it. Nothing we know suggests that this should not be the case. However, an unusual feature of COVID-19 is that some fraction of people infected with the virus do not display symptoms, while being able to infect others. About 30-60% of those infected, perhaps more, are such asymptomatic carriers of infection. Why this is so is still unknown. The supermodel takes a new route that virtually no other model takes. It assumes that the population prior to infection can be divided into two separate parts. One part will always be either asymptomatically infected while the other will always exhibit symptoms. The supermodel assumes that “immunity levels, genetic disposition and co-morbidities” might determine this assignment. The truth is, we just don’t know this.

Testable consequence

This choice, however, has one specific testable consequence. If we took a random sub-set of people, say healthcare workers drawn from the general population, we should then expect to see the same proportion of asymptomatic versus symptomatic patients in them as in the general population.

This is not what is seen. Around the world, healthcare workers are at more risk of severe infection and death than members of the general population. This suggests that it is the amount of exposure to the virus that may be important in determining whether an individual will exhibit symptoms.

More parameters

A second point is the following: A model should have as few numbers as possible that must be provided by the modeller to describe the data (they’re called parameters). For virtually all such models, such parameters must be estimated. The more the number of parameters, the larger the significance of uncertainties in these numbers, even as more parameters provide more flexibility. The supermodel ostensibly has just four parameters. It fits the count of new cases well, reproducing the recent peak in Indian cases as well as the two peaks that Delhi saw.

Let’s dig a little deeper. The model divides the period between the start of the pandemic and the date at which the results were obtained into six parts. These four parameters all take different values in each of these parts. This gives 24 parameters in all, all separately varied to fit the case count. These parameters are not constrained in any way by an understanding of COVID-19 epidemiology.

Worse, some of the parameters are then varied across a large range, from 67 to 4,75,000 in one case. There is no justification provided for this. It makes little sense to have so many parameters, all changing, in a model. Indeed, a famous quote from the mathematician John von Neumann applies here: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk”.

Lives at stake

There are many more problems with both the model and the conclusions it arrives at. However, just this discussion should indicate that the government’s supermodel is ill-suited to address questions of COVID-19 spread in India. Basing public health policies on models that are flawed is dangerous, since the lives of people are at stake and false optimism carries risks with it. Science should not serve political ends.

There are better models. Choosing this one to be India’s ‘supermodel’ presents a misleading picture of India's capabilities in both epidemiology and modelling, to Indians as well as to the rest of the world.

(Gautam I. Menon is a Professor of Physics and Biology at Ashoka University, Sonepat, and at the Institute of Mathematical Sciences, Chennai.)