AUTHOR=Demongeot Jacques , Ouangko Haiwe Adam , Diarra Maryam , Gofti-Laroche Leila 

TITLE=Forecasting epidemic peaks with the index of dispersion of new cases

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 11 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1670077

DOI=10.3389/fams.2025.1670077

ISSN=2297-4687

ABSTRACT=IntroductionThe epidemic transition that took place in Europe and North America during the twentieth 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.MethodsMost of the highly sophisticated mathematical models currently in use have failed 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 simpler but robust mathematical models that are more in line with the basic principles governing the interactions of microorganisms with their hosts, in a given environment and exposure conditions. For this reason, we will use the Bernoulli model and the parameters related to the empirical distribution of new daily or weekly cases observed.ResultsUsing the empirical distribution of new cases and the revisited SI model, we have studied the predictive power of the dispersion index of new cases and the applications proposed to illustrate our approach concern the Covid-19 epidemic in various developed and developing countries as well as the Dengue epidemic in the French Antilles. The results obtained show that, except in cases where the occurrence of vaccination reduces its anticipation capacities, the dispersion index has a predictive power of the occurrence of epidemic peaks.DiscussionOne limitation of this study is that it is based on official data that is sometimes affected by changes in health policies (recommendations, monitoring indicators, data collection methods, etc.), but we believe that the impact on the quality of the demonstration remains moderate or even modest.