How concepts and ideas from Statistical and Climate physics improve epidemiological modelling of the COVID 19 pandemics

In the past two years, numerous advances have been made in the ability to predict the progress of COVID19 epidemics.  Basic forecasting of the health state of a population with respect to a given disease is based on the well-known family of SIR models (Susceptible Infected Recovered). The models used in epidemiology were based on deterministic behavior, so the epidemiological picture tomorrow depends exclusively on the numbers recorded today. The forecasting shortcomings of the deterministic SEIR models previously used in epidemiology were difficult to highlight before the advent of COVID19  because epidemiology was mostly not concerned with real-time forecasting.  From the first wave of COVID19 infections, the limitations of using deterministic models were immediately evident: to use them, one should know the exact status of the population and this knowledge was limited by the ability to process swabs. Futhermore, there is an intrinsic variability of the dynamics which depends on age, sex, characteristics of the virus, variants and vaccination status. 

Our main contribution was to define a SEIR model that assumes these parameters as constants could not be used for reliable predictions of COVID19 pandemis and that more realistic forecasts can be obtained by adding fluctuations in the model. The fluctuations in the dynamics of the virus induced by these factors do not just add variaiblity around the deterministic solution of the SIR models, the also introduce another timing of the pandemics which influence the epidemic peak. With our model we have found that even with a basic reprdocution number R_t less than 1 local epidemic peaks can occur that resume over a certain period of time. 

Introducing noise and uncertainty allows  to define a range of possible scenarios, instead of making a single prediction. This is what happens when we replace the deterministic approach, with a probabilistic approach. The probabilistic models used to predict the progress of the Covid-19 epidemic are conceptually very similar to those used by climatologists, to imagine future environmental scenarios based on the actions taken in the present.  As human beings we can intervene in both systems. Based on the choices we will make and the fluctuations of the systems, we can predict different responses. In the context of the emergency that we faced, the collaboration between different scientific fields was therefore fundamental, which, by comparing themselves, were able to provide more accurate answers. Furthermore, a close collaboration has arisen between epidemiologists and climatologists. A beautiful synergy that can give a great help to society in a difficult moment.

References

-Faranda, Castillo, Hulme, Jezequel, Lamb, Sato & Thompson (2020). Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(5), 051107.

-Alberti & Faranda (2020).  Communications in Nonlinear Science and Numerical Simulation, 90, 105372.

-Faranda & Alberti (2020). Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(11), 111101.

-Faranda, Alberti, Arutkin, Lembo, Lucarini. (2021).  Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(4), 041105.

-Arutkin, Faranda, Alberti, & Vallée. (2021). Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(10), 101107.