By Gabriela Cybis
How mathematical modeling deals with the spread of viruses, from corona to zombies
As soon as a viral epidemic arises, information about the number of new cases and deaths begins to be released, and the cities where the infected are found – first concentrated near the point of origin, and gradually spreading in a wave that threatens to take hold. the globe. In recent years we have seen this film a few times: in 2002, the SARS that spread to seventeen countries; in 2009, swine flu (H1N1) which became pandemic reaching all continents; in 2013, the threat of bird flu. And now we are following the development of the new coronavirus epidemic.
What can be done to stop the spread of the virus? Governments take measures such as closing schools; measure the temperature of passengers disembarking at airports; prohibit the entry of people from affected regions; restrict air traffic; cancel large public events, such as Chinese New Year celebrations. But how to assess the real effect of these actions? Considering the economic and social impact of these restrictive measures, does the gain in terms of containing the epidemic pay off?
The answer to these questions is complex and depends on a number of factors. Not all viruses are the same, and their mode of transmission, the ease with which they infect new people, latency periods and lethality vary. In addition, social, demographic and even climatic conditions can affect the dynamics of the virus.
As we do not have a crystal ball, the best way to understand how these factors combine to determine the course of the epidemic are the mathematical models that usually divide the population into three subgroups: susceptible (those who never caught the disease and, if they come into contact with she can contract it); infectious (those who carry the virus and, if they come into contact with susceptible people, can transmit it); removed (those who no longer participate in the dynamics of infections, because they have either recovered – and are immune – or have died).
To study the progress of the epidemic and outline containment strategies, the models follow the network of interaction between these groups, in varying degrees of detail. In the United States, for example, a model for influenza-like illness uses census data, taking into account maps, walking patterns, age and interactions at work, school and at home. This simulates a huge environment in which agents (individuals) follow their routines in a similar way to The Sims. Each time a susceptible individual interacts with an infectious person, he is likely to contract the infection. The simulation is repeated several times to identify the most likely course of the epidemic and the results of control interventions.
An important caveat is that the model is only as good as its assumptions. If it does not capture the virus transmission process well, the findings will reproduce these flaws.
After all, what have we learned from these studies? Randomness plays an important role in the course of various epidemics. Models can give us vaccination strategies in age groups, for example, favoring children, since the school environment is conducive to the circulation of the virus. Combined proposals, with actions such as strategic distribution of antivirals, changes in individual behavior and selective closure of schools can achieve a high degree of success.
Certain strategies (the gathering of professionals from the scene of the epidemic, among others) may have the opposite effect to that desired. And, of course, it all depends on the specific conditions of the virus in question. The important thing is that we have scientific tools to help us evaluate the effect of each action, acting almost like a crystal ball that helps us to glimpse the result of each choice (and its margins of error).
At the interface between pop culture and epidemiological modeling, who do we find? The zombies. Tradition says that humans bitten by zombies end up becoming zombies. They fit perfectly into the susceptible (human), infectious (zombie) and removed (dead) model, and make up a playful case for teaching these models to new generations of epidemiologists.
Gabriela Cybis is a biologist, professor of statistics at UFRGS, working in statistical modeling for genetics
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