In this study, the chaos theory was first used to model the outbreak of Covid-19 in China, and then in Japan, South Korea and Italy. All the models obtained were used to establish scenarii in other countries, in particular in France, Spain, Belgium and the United Kingdom. In epidemiology, most commonly used approaches rely on a priori knowledge. In the context of an emerging virus epidemic, knowledge about the disease and its propagation can be quite limited. Consequently, it seemed useful to compare classical epidemiological models to alternative approaches. The chaos theory approach used in the present study offers several advantages. In particular, it is directly based on observations and therefore does not require any strong assumption. In the present situation, despite the shortness of the available time series to model the dynamics of the outbreak, it was possible to foresee with some advance the evolution of the outbreaks in several countries. Among the results, the analysis enabled to obtain a chaotic model very early for China (on February 5th), suggesting that without control the outbreak would have continued its expansion. A non-chaotic model could be obtained for Italy on March 26th enabling preliminary forecasts of the ending stages of the epidemic in Italy and France. Finally, the analysis showed that the extent of the outbreak was directly linked to the earliness of the control measures.


Figure 1 : Epidemiology evolution for Japan (J), Germany (G), France (F), Spain (E), Iran (I), Italy (I), South Korea (K), United Kingdom (UK), United States (US),   in terms of reference scenario. Nine scenarii are considered ranging from light (Japan first epidemic phase) to the most severe (Italy). Most countries went through a fast evolution. Japan totally overtook its initial scenario to reach a situation between that of Korea and that of the Hubei province. Spain overtook Italy to stabilize slightly above it. K also went further and is not yet stabilized . The same applies to the US whose scenario is getting close to that of Italy and is very likely to be even worse. (NB this is the situation when this is written, subject to change!)

For more info see : Mangiarotti, S., Peyre, M., Zhang, Y., Huc, M., Roger, F., & Kerr, Y. (2020). Chaos theory applied to the outbreak of COVID-19: An ancillary approach to decision making in pandemic context. Epidemiology and Infection, 148, E95, 1-9. doi:10.1017/S0950268820000990.

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