[LUM#13] Top Models
Understanding how an epidemic spreads in order to help control it is the contribution of mathematical epidemiology. This discipline has been widely embraced since the very beginning of the COVID-19 pandemic. Mircea Sofonea, Professor the Mivegec* laboratory, sheds light on this approach, which has perhaps never received so much media attention.
“Basic reproduction number, R zero.” A term that has been on everyone’s lips since the start of the COVID-19 pandemic—and one you may never have heard before. This famous R0 is the key figure in a field that has been in the spotlight for the past few months: mathematical epidemiology.
“The intersection of mathematics and public health dates back to the 18th century,” explains Mircea Sofonea, Professor the Infectious Diseases and Vectors Laboratory: Ecology, Genetics, Evolution, and Control. At that time, Europe was grappling with smallpox. To combat this dreaded disease, a technique originating in Asia involved inoculating healthy people with the virus taken from mildly ill individuals. The goal was to protect patients from severe smallpox. It was a rather risky method, since variolation—the precursor to vaccination—was responsible for fatal cases of smallpox in some patients.
Develop models
How, then, could one determine whether this approach should be encouraged to ensure collective protection despite its collateral victims? “It was difficult to consider vaccinating an entire village just to compare mortality rates with those of another unvaccinated village, for example; that would not have been ethically acceptable, ” explains the researcher in epidemiology and the evolution of infectious diseases. The only alternative was to develop models. “That is, simplifying reality to answer a specific scientific question.” ” In 1760, the Swiss physician and mathematician Daniel Bernoulli developed one of the first such models. Based on the study of differential equations, he estimated that mass variolation would result in a 3-year increase in life expectancy. “That was the starting point of 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 in high demand regarding COVID-19. To better describe the epidemic, researchers estimate the well-known basic reproduction number R0, which reflects a disease’s potential for spread. “Biologically, it corresponds to the average number of people infected by a single contagious individual. This figure characterizes the trajectory of the epidemic: when it is greater than 1, the epidemic spreads, and when it is below 1, it is under control, ” explains Mircea Sofonea. The researcher and his team estimated R0 in France at the start of the epidemic to be between 2.5 and 3.5. According to their model, R0 fell to 0.7 during the lockdown, which significantly reduced interpersonal contact.
Behavioral lever
“In the absence of a pharmaceutical solution, behavioral measures—particularly physical distancing—are our only weapon against infectious diseases,” explains the epidemiologist. This, in particular, 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 customs, physical proximity, frequency of handwashing, and spontaneous mask-wearing.”
While we wait for a treatment, the focus is entirely 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 strategy to apply to the epidemic during the first 100 weeks, “which is the estimated time needed to discover and implement a treatment or vaccine.” They thus developed a theory of optimal control. Its strategy? To rapidly implement strict control measures and then gradually ease them. “Our models suggest that this strategy would effectively contain the epidemic over the period in question. It would yield better results than no control measures at all, but also better than a strategy of constant strict control.”
Consultation
Can these models dictate the measures that should be implemented? “We must be cautious in using them and not rely on a single simulation,” responds Mircea Sofonea. “These models have no predictive value beyond the short term, but they are part of the decision-making toolkit. And the choice of strategy to contain an epidemic must be made in consultation with other disciplines: epidemiology, medicine, and the humanities and social sciences must collaborate to propose the best measures for policymakers to implement.”
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*Mivegec (UM-CNRS-IRD)