Forecasting epidemic peaks with index of dispersion of new cases

Jacques Demongeot^1*Haiwe Adam Ouangko¹Maryam Diarra²Leila Gofti-Laroche³

• ¹Université Grenoble Alpes, Saint Martin d'Hères, France
• ²Institut Pasteur de Dakar, Dakar, Senegal
• ³Centre Hospitalier Universitaire Grenoble Alpes, Grenoble, France

The epidemic transition that took place in Europe and North America during the 20th century, with the historical decline of infectious disease epidemics, gradually diverted physicians' attention from the world of "microbes." However, recent epidemics have made the surveillance of new microorganisms, particularly viruses, in the general population a new public health priority. Most of the highly sophisticated mathematical models currently in use have often struggled to accurately predict and describe the latest emerging epidemics (mad cow disease, H1N1, swine flu, Covid-19, etc.). Predicting the occurrence of an epidemic remains almost as challenging today as it was in 1760, when D. Bernoulli defined the notion of endemicity and successfully proposed his famous SI equation to describe epidemic dynamics, then applied it to smallpox epidemics. Finally, it might be more interesting to return to the historical, more pragmatic approach, especially in a context of uncertainty, by favoring a simple but robust mathematical approach based on the empirical distribution of the new cases and its dispersion index, more in line with the basic principles governing the interactions of microorganisms with their hosts, in a given environment and exposure conditions. Using the empirical distribution of new cases and the revisited SIRS model, we study here the predictive power of the dispersion index of new cases. The applications proposed to illustrate our model concern the Covid-19 epidemic in various developed (France, Japan, United Kingdom and USA) and developing countries (Brazil and Senegal) as well as the Dengue epidemic in the French Antilles.