The networks behind the coronavirus spread

Mathematical models of epidemiology with inputs from human mobility data give important leads for decisions about quarantine mechanisms

Published: 11th March 2020 04:00 AM  |   Last Updated: 11th March 2020 04:10 PM   |  A+A-

AMIT BANDRE

The threat of infection from the coronavirus causing the COVID-19 disease has gripped the entire world. It was first reported in December 2019 from Wuhan in China. By now, more than 1,15,800 people in over 90 countries have been infected by the deadly virus and at least 4,000 have died. In India, over 50 cases of coronavirus infections have been confirmed. The global scale of the spread of the disease has resulted in immense economic losses due to shutdown of cities, airports and factories, travel bans and quarantining of people. 

With no approved drugs or vaccines available to fight the virus at present, it is virtually enjoying a free run, impeded only by the quarantine measures adopted in China and elsewhere. This free run is largely aided, ironically, by the modern networked societies that we live in. If not for the network effect, the coronavirus could not have infected people in places thousands of kilometres apart such as Wuhan, Milan and Chicago in different continents within one month. It might seem paradoxical that faster means of communication through the network of roads and air routes also helps in faster transmission of the disease as well.

By the end of 2002, Guangdong province in China was encountering the first cases of what came to be called the severe acute respiratory syndrome (SARS). SARS is also caused by a form of coronavirus. It became a global epidemic because travel networks played a critical role in transmitting the infection. Professor Liu Jianlun from Guangdong visited Hong Kong in February 2003 and, unknown to himself, became the carrier of the SARS virus. He infected several people in the hotel where he was staying. In a few weeks, the infection had spread to places as far as Hanoi and Toronto.

SARS infected around 1,000 people in the initial four months, but the current coronavirus is much faster, having affected 1,200 people in less than a month. Invariably, the speed of infection transmission through human contacts is tied to the speed of our transportation systems. More than 2,000 years ago, circa 430 BC, Athens was faced with a major epidemic (probably a plague or typhoid) that transmitted through humans and killed almost one lakh people. Yet, in an era when the transport networks were not as efficient as they are today, the epidemic did not become a global threat. By the 14th century, when a plague hit Europe, trade and travel networks had developed sufficiently well. This bout of plague infection originated in Mongolia in Asia and reached as far as England in about seven years through the trade routes. The medieval Latin historical text Chronicon Angliae Petriburgense recounts the Black Death devastation: “... it came to England and first began in the towns and ports joining on the eacoasts, and made the country quite void of inhabitants.” An Italian memoir by Gabriele de Mussi in 1348 claims that plague-infected dead bodies of solidiers were lobbed into the Crimean city of Caffa (now called Feodosia). This possibly marks the first use of biological warfare. Although over three crore people died due to Black Death, many towns and villages in Belgium, Netherlands and parts of Spain with little connectivity were spared from the plague visitation. The harbours at Bombay and Calcutta are blamed for the entry of plague infection that killed lakhs of Indians from 1898 to 1908. The Surat plague in 1994 did create panic, but did not spread very far.

In times of public health crises, the network of trade and transport routes is an important parameter in predicting how an infection is transmitted through a population. Mathematical models of epidemiology, or the science of infection distribution, date back to almost a century. Today, more advanced models with additional inputs from human mobility data provide important leads for decisions about initiating quarantine mechanisms. For instance, according to the latest model predictions, Hong Kong and Seoul are the highest risk airports for importing the virus from China. In contrast, the risk factor of Indian airports is quite small. This correlates with the current perception that India, even with more than 50 confirmed cases, is not among those most affected by the coronavirus.

In general, a mathematical framework for networks can provide such quantitative information about disease spreading based on connectivity patterns among human settlements. Networks were first studied in the 17th century by the Swiss mathematician Leonard Euler and later developed in the 20th century by the Hungarian mathematician Paul Erdos. Interestingly, the mathematical equations used for elucidating disease spreading through networks can also, with some changes, describe how fake news and rumours evolve on social media.

In early 2019, when Prime Minister Narendra Modi visited Tamil Nadu, Twitter hashtags #GoBackModi and #TNWelcomesModi were both trending. An analytics report nailed these hashtags as the handiwork of bots, not human users. Such fake influences on social media are hard to beat. A recent research published in the prestigious journal Science tracked down millions of Twitter posts and found fake news and rumours spread faster than truth. In fighting fake news, we are in for the long haul. In contrast, coronavirus might be contained, even if not entirely eliminated, by a combination of quarantining, hygiene measures and possibly medicines.

M S SANTHANAM
Physicist and a professor at the Indian Institute of Science Education and Research, Pune. Views expressed are personal Email: santh@iiserpune.ac.in



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