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The Hindu Explains | How are mathematical models being used to predict the dynamics of the SARS-CoV-2 virus?

Shoppers at the Patel Bazar bangles market in Jammu on October 23, 2020.   | Photo Credit: PTI

The story so far: The India National Supermodel Committee, constituted by the Department of Science and Technology (DST) and consisting of mathematicians, computer scientists and medical professionals, recently announced that India had passed its ‘COVID-19 peak’ in September and that active infections by the SARS-CoV-2 virus would fall to a ‘minimal’ level by February. The conclusions were arrived at with the help of a mathematical model.

What is the ‘National Supermodel’?

When the DST said in May that it had convened a group to track the evolution of the pandemic, it viewed the ‘supermodel’ as one that would aggregate the ‘best of’ existing mathematical models, and hence the name. From February to March, when the relative numbers of infections were low everywhere in the world except China, scientists began estimating the beginning and the course of the pandemic in their countries through mathematical modelling. Using differential equations, that show how multiple variables, such as infections and deaths vary with respect to one another on different parameters, modellers try to estimate the fraction of the population which is infected at a particular point in time.

Comment | Has India passed the COVID-19 peak?

How are the predictions arrived at?

One of the models used is the susceptible-infected-recovered (SIR) model, which divides a given population into three groups: ‘susceptible’, ‘infectious’, and ‘recovered’. Over time, the number of people in each group change. The number of ‘susceptible’ people is highest at the beginning of the pandemic, for example, since everyone who is not infected is considered susceptible in most cases. At this point, the number of infectious individuals is at its lowest. As time passes, the number of susceptible people decreases, the number of infectious people increases. This model assumes that at any given point of time, an individual in a defined population will be a part of one of these groups.

The model’s output is dependent on what is fed into it. In the early months, little was known about the incubation period of the virus, the reproduction number (how many people an individual could infect), how lethal it was, etc. These led to oversimplified projections.

With time, data accumulated and improved the models. In the absence of cold numbers, modellers are forced to draw assumptions — on how quickly the disease spreads, the varying susceptibility of adults as opposed to children, for instance — which are a mix of judgment and luck. A key differentiator in the ‘supermodel’ was that it purported to account for asymptomatics.

Also read | Problems with the Indian supermodel for COVID-19

What are the major findings?

While the modelling committee was a seven-member group, a scientific paper describing the group’s work and published in the Indian Journal of Medical Research has only three authors — a physician, a mathematician and a computer scientist. The modelling exercise also attempted to hypothesise on what India’s caseload would have been in the absence of a lockdown, or if it were delayed by a few weeks or a month after March 23. The first lockdown came into effect on March 25. If there were no lockdown, the number of active infections would have peaked at 14+ million and the peak would have arrived by mid-May. “There was little qualitative difference between two lockdown timings of April 1 and May 1, 2020. This would have resulted in a peak between 0 and 5 million active infections by mid-June. If there was no lockdown, it would have resulted in more than 2 million deaths. The two lockdowns (April 1 and May 1, 2020) would have resulted in 0.5-1 million deaths. The number of deaths with current trends is projected to be less than 0.2 million,” the authors say in the paper.

Comment | Imperatives after India’s September virus peak

Is it credible?

The model’s declaration of India having passed its peak comes nearly a month after the reported date — September 17 — from when the national caseload started to decline. From adding nearly 90,000 cases every day in early September, India is now adding around 55,000 cases daily. It is not clear whether, or how often, the mathematical curve that shows the modelled rise and peak of the number of cases has been adjusted to fit the actual number of cases.

The authors say the model expects a decline and virtual extinguishing of the pandemic by February, on the assumption that existing guidelines on restricting public gatherings, wearing masks, etc., continue and no major mutations making the virus more infectious take place. The authors have relied on data from a popular, crowd-sourced database, ‘’, and acknowledge that “...the major limitation in their model was the non-availability of accurate data”. Officials from the Health Ministry have been non-committal about India passing the peak, but admit that mathematical models have their utility in terms of planning.

Coronavirus | September accounted for 41.53% of total cases in India

How have similar mathematical models of the pandemic fared?

The United Kingdom adopted a policy of not imposing movement restrictions, except on the elderly, and letting the virus run wild through the population to acquire ‘herd immunity’. This changed after an epidemiological model said that one in two Britons would die with such a policy. India, too, relied on a rudimentary model in April to estimate that the pandemic would die out by May 16 because of the first lockdown. Mathematical forecasts, unlike, say, climate modelling, once publicised, can influence behavioural change, and this affects the model’s prediction. It derives from a standard aphorism in statistics that “all models are wrong, but some are useful”. Independent critics have said such models, at best, lay out what could happen in the next two weeks and it would be foolhardy to foresee months ahead.

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Printable version | Nov 30, 2020 4:50:21 AM |

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