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Photo: iStock

Covid-19: Can mathematical models help us navigate the pandemic?

From lockdown exit strategies to simulating the spread of a virus, how predictive models work during pandemics

If you were to look at the two main facets of the covid-19 pandemic, you wouldn’t have to look beyond numbers. First, the rising number of infections globally (more than five million) and death toll (more than 350,000). Then, the covid-19 R-0 (r-naught) value, which is the reproduction number of the virus that tells you how infectious the novel coronavirus is. Will the disease spread? How many people could get infected and how many could die? The answers to all these rest with the R-0.

But there’s another side: Numbers and mathematics can be used to chart a course through the pandemic and predict what comes next. Earlier this month, researchers from Israel’s Weizmann Institute of Science explained an exit strategy that uses simple mathematics to leverage the virus’ latency period. This mathematical model, known as the 10-4 system, would have economies restart in a staggered manner, with certain sections of people being allowed to step out while others remain indoors. This cycle would be repeated with a different set of people.

A brief from WeizmannCompass, a portal which showcases the latest breakthroughs from the institute, explains that this approach calls for lowering the rate of infection through a cyclical opening of schools, businesses and workplaces. “According to this model, discrete sectors of the population would be allowed to leave home and resume their normal activities for a period of four days, while observing coronavirus safety stipulations such as the use of masks and maintenance of social distance. At the end of each period of free movement—during which there would be increased coronavirus testing among the working population—such individuals would return home to observe a full lockdown of 10 days before venturing out again."

The thinking behind this? Research on many reported cases of covid-19 around the world has shown that the virus has an average incubation, or latency, period of two-three days. The model seeks to use this period, during which the virus cannot be passed on to others.

In a recent New York Times piece, two Weizmann Institute professors, Uri Alon and Ron Milo, explained how this model could check the covid-19 virus’ R-0, or reproduction rate, and “could suppress the epidemic while allowing sustainable economic activity". “Even if someone is infected, and without symptoms, he or she would be in contact with people outside their household for only four days every two weeks, not 10 days, as with a normal schedule. This strategy packs another punch: It reduces the density of people at work and school, thus curtailing the transmission of the virus," they write.

In India, the Indian Scientists’ Response to CoViD-19 (ISRC), a group of over 500 Indian scientists and researchers, has developed a simulation framework to model the spread of covid-19 in India. It’s a first of its kind, state-specific epidemiological compartmental model that lets you generate “what-if scenarios" under various conditions of non-pharmaceutical measures for different regions. The online model, called INDSCI-SIM, can be used to mathematically calculate the spread by taking into account different parameters and interventions: the R-0 value, type of lockdown, and so on.

“We stress a different approach, proposing that an asynchronous, periodic lockdown in which only a third of the working population goes to work for short periods at a time is likely the best way of returning people to work when emerging from the lockdown," says Gautam Menon, professor of physics and biology at Ashoka University, on email.

At a webinar earlier this month, Prof. Menon, who has a long-standing interest in the modelling of infectious disease and its implications for public policy, explained the INDSCI-SIM model further. One of the ideas was to synthesize data from various sources and provide a benchmark set of rates that other people could use to model covid-19 in India. The model, he added, also aims to simulate the spread of covid-19 at the state and district levels, while including parameters like demographics and migration.

Predictive mathematical models have proved useful in the past, especially when there are no pharmaceutical interventions for an infectious disease. In the case of covid-19: a drug or vaccine.

That makes these models all the more important in the near future, says Prof. Menon. “They have shed light on things that we could have chosen to have done which can be shown, through models, to have little effect. Quarantines, for example, have been shown to have little effect beyond delaying epidemic spread. The modelling of international travel networks has been a powerful tool in helping us understand how and in what sequence a pandemic spreads across the world, as in the H1N1 pandemic," he says, adding that predictive models for the short term can be trusted to indicate, for instance, strains on the health system, the growth of hot spots, and how best to target testing and other measures.

So how can public authorities leverage these models? Jahnavi Phalkey, a science historian and director of Science Gallery Bengaluru, says that while numbers are the only way to get a grasp over the situation and take action on public health, the task of public health authorities is far more social than research-related. “At the end of the day, while it is founded on sound scientific principles, the information you have to give people is about their behaviour and the expectations you have from them is also about behavioural changes," she adds. “A lockdown was the obvious and necessary thing to do. It delays the onset of huge numbers of infection.... You buy yourself time to be ready for when this escalates."

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