How Mathematical modellers are influencing Covid-19 policies in real time

IT IS AN understatement to say that Jayson Shi Jia’s brain works like a machine gun. For someone who is a sharp conversationalist, this University of Hong Kong business professor seems to be in a perpetual race to think slower to be able to communicate better. “The approach in my paper is very different. We make no assumptions; we observe population movement, and we observe case count and can subsequently extract the relationship between the two to explain spread and growth of Covid-19,” says the co-creator of a mathematical model for planning the fight against the highly infectious viral disease.

Jia and three others that make up his team had sprung into action as early as February to develop a model showing that data on population movement (which they got from a major Chinese telecom carrier) can accurately track the spread of the SARS-CoV-2 virus. Their paper was submitted to Nature on February 14th. Besides, he says, he and his colleagues have formulated a new kind of modelling “that can keep track of Covid-19 risk to identify high-transmission-risk locales at an early stage”.

The most tempting part is that his method can be applied in any country with mobile phone data and does not necessarily need apps or smartphones. Their primary work for creating projections about the disease’s spread started with using countrywide data “tracking all movement out of Wuhan between January 1 and January 24”. He avers, “We included all individuals who spent at least two hours in Wuhan during this period [since the city is a major transport hub]: this yielded a count of 11,478,484 people leaving or transiting through the prefecture of Wuhan between January 1 and 24.”

Epidemiologists and other scientists have sought help from mathematicians for a long time now to arrive at meaningful conclusions about the data they have at their disposal. Now with data available in large numbers, the practice has gained momentum. For instance, in Japan, epidemiologist Kenji Mizumoto and three of his co-researchers worked on a project that estimated the asymptomatic proportion of Covid-19 cases on board the Diamond Princess cruise ship that had left Japan on January 20th and had to cut short its trip after a passenger tested positive. The ship, which had been quarantined in Yokohama since February, has now left for Malaysia.

Some models have rightly captured the pattern of the disease while others have gone far off the mark. In India, a senior official of NITI Aayog, the Indian Government’s policy think tank, had said on April 15th that the number of Covid-19 cases would slow down by May 16th. Dr VK Paul, Member of NITI Aayog and acclaimed paediatrician, meanwhile, told Open that there was never an assertion of infections falling to zero as claimed in some reports.

Similarly, in Britain, an Imperial College research led by mathematical epidemiologist Neil Ferguson published in mid-March has now attracted widespread criticism for a faulty code used for the study. The report said, ‘In the most effective mitigation strategy examined, which leads to a single, relatively short epidemic (case isolation, household quarantine and social distancing of the elderly), the surge limits for both general ward and ICU beds would be exceeded by at least eight-fold under the more optimistic scenario for critical care requirements that we examined. In addition, even if all patients were able to be treated, we predict there would still be in the order of 250,000 deaths in GB, and 1.1-1.2 million in the US.’ His report added that a completely unmitigated epidemic could cost 510,000 lives in the UK and 2.2 million in the US. It was largely this study that forced the British government’s hand to opt for a lockdown. Analysts later found that the model the now-tainted Ferguson based his calculations on was decades-old.

Nevertheless, the likes of Jia continue to stand vindicated. These mathematical researchers are busy writing codes, analysing data and making projections about the trajectory that the Wuhan-originated pandemic would take in various parts of the world. Other models—such as the one created by infectious diseases modeller Kiesha Prem and others—on the effects of control strategies have turned out to be useful for politicians and bureaucrats in reducing contacts in school and work and at the same time building healthcare capacities to mitigate a second crisis. Incidentally, one of the reasons cited for the unexpected spread of infections in the UK was that they had never thought it wise to shut down schools. Schoolchildren recovered from the disease or showed no symptoms, but infected older members of the family, putting the country’s health system on its toes.

Chasing a pandemic
A patient gives samples for swab test at Guwahati Medical College Hospital, May 17 (Photo: AP)

Another model for comprehending the dissimilar spread of disease in China and Western countries, developed by physics PhD student Bnaya Gross and others, also found wide acceptance among scientists and analysts. It divides the disease spread in two stages. In the first stage, within a few days, the infection rate in a city is close to constant probably due to the lack of means to detect infected individuals before symptoms are manifest. In the second stage, the infection rate goes down exponentially due to quarantines. While most cities in China enforced quarantines even before symptoms became evident in the infected population, other countries were not able to do so early on in the infection cycle, probably due to less control on social interactions and overloaded health systems.

Some models seem to strike a chord with analysts in India as well. Jia tells Open, “There are many different mathematical models. For example, ‘math’, the way lay people generally see, it is a pure math model [which is really rare nowadays], or a simulation model [which only requires assumptions and no real data]. As computing power has improved over the decades, statistical approaches based on empirical data are more common [empirical modelling]—this has many subtypes too.”

He adds, “When you read about ‘big data’, it usually relates to ways in which empirical modelling is done and, in particular, methods for calculating it.” Jia goes on to explain that all these are methodological points—what is most important in science is actualising an idea that is meaningful. “You will find many impressive mathematical models or methods of computing models floating around, but often, the basic idea or research question behind them isn’t the most interesting.”

Each epidemic is different and whoever is confronting a new one is doing it as though it is their first. Which is why mathematical models ought to factor in the novelty about any new disease, especially a pandemic. A completely reliable mathematical model of a new viral epidemic is extremely difficult to make because many things are still unknown about the virus

As regards Covid research, Jia says, “You’ll see a lot of metapopulation models like SIR and SEIR, which are kind of like simulations based on assumptions of epidemiological spread. They are probably the most common type of research out there. Researchers have also combined the models with outside data sources [so that there are fewer assumptions one has to make].” Jayson S Jia along with Jianmin Jia of Chinese University of Hong Kong, Shenzhen, and Nicholas Christakis of Yale University, US, will explore applying his model to other countries and extending it to situations where there are multiple Covid-19 hotspots.

Renowned mathematical epidemiologist Fred Brauer has written extensively about the history of diseases and data. Currently Professor Emeritus at the University of Wisconsin-Madison and Honorary Professor at the University of British Columbia, Canada, Brauer is the co-author of Mathematical Methods in Epidemiology. In an article titled ‘Mathematical epidemiology: Past, Present, and Future’, he writes that the study of infectious disease data began with the work of John Graunt (1620-1674) with his 1662 book Natural and Political Observations Made upon the Bills of Mortality. He notes that what is usually described as the first model in mathematical epidemiology is the work of Daniel Bernoulli (1700-1782) on inoculation against smallpox. Brauer commends Ronald Ross ‘for his demonstration of the dynamics of the transmission of malaria between mosquitoes and humans’. Of course, the use of maths in disease control, suppression and mitigation has evolved rapidly over time.

Increasingly, mathematical researchers are aligning with epidemiologists and consultants to create models that could be adopted by countries, including India, bracing for easing restrictions to restart businesses and public services.

Eran Yashiv is one of those who shot into the limelight recently with his highly attractive proposal for a back-to-work option. This professor of economics at Tel Aviv University in Israel and the London School of Economics and Political Science’s Centre for Macroeconomics has collaborated with biologists Uri Alon and Ron Milo at the Weizmann Institute of Science in Israel promising a model to end the lockdown by reducing damage to the economy and by saving lives. He has often noted that widespread testing is a far cry in many countries and so the best way, according to him, is to exploit a ‘blind spot’ of the coronavirus. He and his team call it the 10-4 formula. It involves working from home for 10 days and from office for the next four days. Their logic is that even if someone is infected while at work, they would start displaying symptoms during the 10-day break. Speaking to Open, Yashiv admits that asymptomatic cases can throw such an assumption out of gear. Talking of the idea of this work cycle, he says, “My Weizmann colleagues worked since February-March; I joined in April. I’m trying to analyse the economic mechanisms and to disseminate the idea to policymakers around the world. It was they who suggested the idea.” He emphasises that in places where the epidemic is weak or minor, policymakers had better do a gradual opening. “Otherwise adopt [the] 10-4 [formula] quickly keeping other measures in place.”

Chasing a pandemic
Emergency workers exit the Diamond Princess cruise ship in Yokohama, Japan, February 10 (Photo: Getty Images)

The truth is that each epidemic is different and whoever is confronting a new one is doing it as though it is their first. Which is why mathematical models ought to factor in the novelty about any new disease, especially a pandemic.
Ajit Haridas, former Chief Scientist at the Council for Scientific and Industrial Research (CSIR), is now part of a think-tank christened Resilient Kerala. Its eight-member team, which includes Singapore-based consultant and entrepreneur Rajasekharan Pillai, has submitted a mathematical model to the Chief Minister of Kerala. Haridas says he personally tracks trends from across the world and the projections his team have made are accurate and in line with figures given out by government agencies. What sets their model apart is that they have calibrated it with data which are more appropriate for India. He reels out a list of countries such as Thailand, Malaysia, the Philippines and others that are similar to India in terms of climate, density of population and morbidity conditions. “Numbers from Italy, Spain and the US cannot be used for forecasting the progression of the disease in India where per capita infections and deaths are far lower,” he tells Open, stressing that data from countries with similar conditions alone can offer us a peek into the future of how the virus would behave.

According to a statement by Resilient Kerala, ‘Mathematical models are the only tools with which we have a chance to predict the future course of the epidemic. A close prediction with granularity is very critical to develop strategies to mitigate the impact of the epidemic and manage resources in the best way possible. The model can predict when the epidemic will peak, how many people will be infected every day, how many will need hospitalisation, how many needs critical care, how many deaths will be there and so on.’ It is here that such models can make a difference to how policies are made. Consultants Open spoke to agree that a lockdown without a concrete plan is ‘not a plan at all’.

The statement adds that a completely reliable mathematical model of a new viral epidemic is extremely difficult to make because many things are still unknown about the virus. ‘However, one way to make the predictions reliable is to calibrate whether the results the model predicts agree with whatever data we already have about the epidemic. And adjust the model till we get good agreement. If we do this on a daily basis and rerun the model, we would get the next best outcome to reality. The model can also develop scenario-based outcomes for you to make decisions on how and when to release lockdowns besides and beyond the existing ‘hotspot’ based strategy,’ the think-tank says.

Haridas believes that only a model that takes into account pre-existing immunity among Indians living in India can offer insights into how Covid-19 spreads in the country. He says that this factor has been taken as an “initial condition” in the model. He reasons that Thailand, which has similar weather and population density parameters, has seen a remarkable pattern in Covid-19 infections. “Thailand received over 2 million Chinese tourists in the early days of the Covid-19 pandemic. Ideally, the country should have had far worse fatalities than Italy or any other country in the West. But now things are almost back to normal there. How did it happen?” he asks, while insisting on the imperative of collecting most relevant data to build predictive models. “If we had used models using data from Britain or elsewhere in Europe, we would have got our calculations completely wrong,” he claims. Haridas also comes up with an interesting correlation although it is his hypothesis: that greater vulnerability of countries such as India and Thailand to influenza may have something to do with higher immunity towards Covid-19. “In England, deaths per lakh due to influenza a year may be in single digits. It is ten times that in India and Indonesia and Thailand,” he states.

Chasing a pandemic

Meanwhile, Roschen Sasikumar, another former CSIR scientist who is currently collaborating with Haridas, explains how their model has been created to ensure best results. Sasikumar, a mathematician who currently teaches primary school children as a serious hobby, says that she wrote the code in the Python programming language. The compartments in their model include susceptible, infected, sick, recovered, critical and dead. Using data available, the team keeps a check on the rate of movement from one compartment to another to come up with observations. “This would help policymakers make prompt decisions on how they should address the pandemic,” she says. Both Saikumar and Haridas contend that India rushed into a lockdown before infections touched the inflection point. “It makes no sense why that should have been done. Now that it is done, models can predict what the next moves of governments could be,” she avers, adding that it is a great experience to write code for an epidemiological initiative that also considers the economic fallout of a lockdown.

As the might of supercomputing, artificial intelligence and Big Data are being unleashed to aid medical research, shape individual and collective behaviour and draft policies to fight a virus, the world is certain to gain new knowledge about how to fight the current pandemic. And yet, even as the supercharged collaborations of mathematical epidemiologists, economists and AI gurus thrive, uncertainty still lingers like a long shadow.

First published in Open

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