[LUM#13] Top models

[LUM Magazine] - Published on December 11, 2020 in Science-Society

Understanding how an epidemic develops in order to help control it is the contribution of mathematical epidemiology. This discipline has been in high demand since the onset of the COVID-19 epidemic. Mircea Sofonea, Professor the Mivegec* laboratory, sheds light on this approach, which has perhaps never been so widely publicized.

"Basic reproduction number, R zero." A term that has been on everyone's lips since the start of the COVID-19 epidemic, and one you may never have heard before. This famous R0 is the key number in a discipline that has been in the spotlight for several months: mathematical epidemiology.

"The intersection of mathematical calculations and public health dates back to the 18th century," explains Mircea Sofonea, Professor the Infectious Diseases and Vectors: Ecology, Genetics, Evolution, and Control Laboratory. At that time, Europe was facing an outbreak of smallpox. To combat this deadly disease, a technique from Asia was used to inoculate healthy people with the virus taken from people who were only mildly ill. The goal was to protect patients from severe smallpox. It was a rather haphazard method, since variolation—the precursor to vaccination—caused fatal smallpox in some patients.

Develop models

So how could we know whether this action should be encouraged to ensure collective protection despite its collateral victims? "It was difficult to consider inoculating an entire village to compare mortality rates with another village that had not been inoculated, for example. That would not have been ethically acceptable, " explains the researcher in epidemiology and infectious disease evolution. The only alternative was to develop models. "That is, simplifying reality to answer a specific scientific question. " Swiss physician and mathematician Daniel Bernoulli developed one of the first such models in 1760. Based on the study of differential equations, he estimated that collective variolation would increase life expectancy by three years. "This was the starting point for mathematical epidemiology," says Mircea Sofonea.

"These models serve three purposes: to understand the past, describe the present, and shed light on the future," explains the specialist, whose team has been heavily involved in the Covid-19 response. To better describe the epidemic, researchers estimate the famous basic reproduction number R0, which reflects a disease's potential for spread. "Biologically, it corresponds to the average number of people infected by a contagious individual. This figure characterizes the trajectory of the epidemic: when it is greater than 1, the epidemic is spreading, and when it is less than 1, it is under control, " explains Mircea Sofonea. The researcher and his team estimated the R0 in France at the start of the epidemic to be between 2.5 and 3.5. According to their model, the R0 fell to 0.7 during lockdown, which greatly reduced individual contact.

Behavioral lever

"In the absence of a pharmaceutical solution, behavioral measures, particularly physical distancing, are the only weapon against infectious diseases," explains the epidemiologist. This would explain why the R0, estimated at 3 in Europe at the start of the epidemic, remained at 2 in Asia. "This difference could be due to lifestyle and cultural differences: greeting habits, proximity, frequency of hand washing, spontaneous mask wearing."

While waiting for a treatment, everything is therefore focused on prevention: "the delicate goal is to contain transmission while being as non-restrictive as possible." But to what extent? To find out, members of the Theoretical and Experimental Evolution team sought to determine the best control measures to apply to the epidemic during the first 100 weeks, "the estimated time needed to discover and implement a treatment or vaccine." They thus developed a theory of optimal control. Their strategy? To quickly implement strong control measures and then gradually relax them. "Our models suggest that this strategy would effectively contain the epidemic over the period considered. It would yield better results than no control measures, but also better than a strategy of strict, constant control."

Consultation

Can these models dictate the measures to be implemented? "We must be cautious in their use and not rely on a single simulation," replies Mircea Sofonea. These models have no predictive value beyond the short term, but they do contribute to decision-making tools. And the choice of strategy to adopt to contain an epidemic must be made in consultation with other disciplines: epidemiology, medicine, and the humanities and social sciences must work together to propose the best measures to implement to policymakers."

*Mivegec (UM-CNRS-IRD)

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