COVID-19: Cancel your next large event, and tell your friends to cancel theirs

Written by Guillaume St-Onge, Vincent Thibeault, Antoine Allard, Louis J. Dubé and Laurent Hébert-Dufresne — March 13, 2020

With football matches being played in empty stadiums across Europe, local authorities closing schools in Spain, the USA and Canada, and bands like Pearl Jam postponing their upcoming tour, COVID-19 is now affecting the day-to-day lives of citizens from countries where the number of cases is seemingly low. When comparing the current number of deaths due to COVID-19 to the more than 300,000 respiratory deaths caused by influenza in a typical year, many wonder whether health authorities are overreacting on a large scale.

They are not.

Epidemics are notably hard to forecast, and no two epidemics are ever alike. This is why the scientific community increasingly turns to mathematical models to better understand the spread of infectious diseases. The pioneering work of Daniel Bernoulli in the 1760s and the groundbreaking studies of the 1920s have evolved in complex computational models thanks to the availability of reliable epidemiological data and to the easy access to ever more powerful computers. Mathematical epidemiology has now earned its lettre de noblesse as an essential tool to assess the potential threat of new pathogens and to help policy-makers design contingency/intervention plans.

And what do mathematical models tell us about the spread of COVID-19?

Projection based on data from China and South Korea, it is plausible that 20% to 60% of the adult population will be infected at some point in time by COVID-19. Even though the very vast majority (approximately 80%) of infected individuals will either be asymptomatic or will have mild symptoms, a small fraction will be sufficiently ill to require intensive care in hospitals. In the USA alone, this could result in tens or hundreds of thousands hospitalizations, overwhelming the health care system and, in the most extreme situations, like in Northern Italy, potentially forcing doctors to choose which patients to save.

The objective behind cancelling events and closing schools is to impede the spread of COVID-19 such that resources to treat the most vulnerable and critically ill will remain available.

Mathematical models tell us that one major benefit of such drastic social distancing measures is to flatten the curve (see image). The rationale behind this statement is that even if the total number of COVID-19 infected people remains the same, new cases could appear more slowly such that fewer people would be sick at any given time. This would decrease the burden on the health care system and thereby save lives.

Another benefit of cancelling large gatherings of people can be understood in terms of the concept of mesoscopic localization, stating in essence that the disease is much more present among large social groups and events, like schools and concerts, than in the overall population. Mesoscopic localization exists somewhere between the micro-, the level of the individual, and the macro-, the whole population. At this level, there are subgroups in the population that can locally sustain the propagation of an infectious pathogen, even if the global prevalence of the disease remains low. The primary effect of cancelling large events and closing schools is to dismantle the large structures in the network of contacts among individuals. These are the ones that facilitate the spread of a pathogen; their removal reduces the total number of individuals that will eventually be infected by the disease.

Another salient feature of the networked nature of human social interactions is the friendship paradox: in our connected world, “your friends, on average, have more friends than you do”. This provides the basis for an efficient way to reach well-connected individuals that are more prone to pass on an infection. An intervention will be driven more efficiently towards well-connected individuals if it follows a random contact than if it picks a random individual.

But all interactions are not equivalent. They depend on the social groups to which the individuals belong, i.e. the higher-order structure of the contact networks. This observation leads to a higher-order friendship paradox: in a structured connected world, “your friends will, on average, belong to more social groups than you do”. Going back to the realm of mesoscopic localization, cancelling large events hereby affect preferentially the more connected individuals through this higher-order friendship paradox. The result is an effective immunization of the remaining vulnerable subgroups not targeted by the intervention, hence leading to an increasing return on the initial intervention.

Structural interventions in the context of localized epidemic is therefore doubly effective. It is like fighting a fire by both removing its fuel and isolating it to prevent new fires downwind.

Individual behavior has a decisive influence on how our societies will manage the current pandemic of COVID-19 and each and every one of us has a responsibility and a role to play. The phenomenon of mesoscopic localization highlights an often overlooked fundamental property of our complex and structured social interactions and suggests a straightforward way to fight the progression of COVID-19: Cancel your next large event, and tell your friends to cancel theirs.

Assistant Professor, Université Laval, Québec, Canada; dynamica.phy.ulaval.ca

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