The French government seems unable to announce or keep dates about the reopening of shops, cinemas, theaters or restaurants. It also struggles to explain why the different sectors of activity are not in the same boat. To these uncertainties is added the permanent surprise of various forecasters about the number of people infected. It would seem that epidemiology and meteorology are sciences which do not obey the same models! But mathematicians wonder about those used until now to predict contamination.
Beyond the standard model
“Mathematical models that can help scientists model the contagiousness and spread of infectious diseases, such as seasonal flu, may not be the best ways to predict the continued spread of the coronavirus,” says Dr Arni Rao, in a press release from the Medical College of Georgia in the United States, where he is a professor of mathematics. Together with his colleagues, they published a letter last December in the journal Infection Control and Hospital Epidemiology. They explain in particular that “these models – of contamination – are even less efficient during periods of confinement or curfew which greatly modify the normal mixing of the population”.
A standard, universal R0 is not possible because the Covid-19 pandemic has not been uniform.
To understand this, we must start from data that we know well now: the R0. This is the basic reproduction rate. The models predict the average number of people who will be infected by someone with the coronavirus. This number is calculated using three main factors: the infectious period of the disease, how the disease spreads, and the number of people an infected person is likely to come in contact with.
Thus, if the R0 is greater than one, infections can become endemic and a larger epidemic or pandemic is likely. At first, the Covid-19 pandemic had an R0 between 2 and 3. However, “while it is never possible to trace every case of infectious disease, the population controls that have become necessary to help mitigate the Covid-19 pandemic have made it difficult to predict the spread of the disease, ”said Dr Rao. “The R0 model cannot be modified to take into account contamination rates which can change from day to day when confinements or curfews are imposed”, continues the researcher. Thus a standard, universal R0 is not possible either because the Covid-19 pandemic has not been uniform in different regions of the world and, of course, within the same country. Some places have different infection rates and on different time frames. Likewise, the “Standard Model” also failed to predict the current third wave of the Covid-19 pandemic.
In the early days, forecasting depended on these traditional methods to understand and anticipate the spread. But, as policies are put in place around civil liberties, the way people relate to each other changes and, with it, traditional patterns. “Different factors are continually changing the basic reproduction numbers at ground level, which is why we need a better model,” says Rao.
That is why he and his colleagues suggest basing forecasts on a dynamic approach using a model called the geometric mean. It is a model that uses today’s number to predict tomorrow’s numbers. The current number of infections – in a given place like the Grand Est or on a city scale today – is divided by the number of infections predicted for tomorrow in order to develop a more precise reproduction rate and above all more current. Like the weather, 2-day forecasts are more reliable than 10-day forecasts!
Precautions for use
Although this geometric method is incapable of predicting long-term trends, it can however more accurately predict the number of probable short-term contaminations which, in an outbreak period (British variant, increase in the number of cases in China, etc.) may prove to be a realistic solution. “Better models have implications for mitigating the spread of Covid-19 and for future planning,” the authors explain. “Mathematical models must be used with care and their accuracy must be carefully controlled and quantified,” they continue. Because any plan of action could lead to a misinterpretation and mismanagement of the disease with disastrous consequences, as has already happened in some countries.