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Mathematical Epidemiology started to be developed since 18th century with Daniel Bernoulli’s work: “Essai d’une nouvelle analyse de la mortalité causée par la petite vérole, et des advantages de l’inoculacion pour la prevenir,” presented to the Paris Real Science Academy in 1760, published in 1765, and considered the zero mark of Mathematical Models in Public Health problems.
From then on, statistical analysis were used to study and clarify interactions and dynamical mechanisms of disease transmission among populations. However, the approach was generally about data interpretation, without predictive models describing possible prospective scenarios.
In the 20th century, the seminal work of Kermack and McKendrick, “Contributions to the Mathematical Theory of Epidemics” (1927), creating compartmental models of population classes divided into “Susceptible,” “Infected” and “Recovered/Removed” individuals, allowed to describe disease propagation by differential equations, enriching the analysis with prediction the effects of parameters as, for instance, vaccination or social distancing.
The start of the 21st century testified a strong development of computational tools and their applications to problems needing large data manipulation, permitting the study of spatial and temporal models described by networks of coupled non-linear differential equations, presenting bifurcations with changing qualitative behaviors under parameter variations.
Combining numerical algorithms and compartmental approach, disease evolutions are studied by complex connected networks identifying population clusters and how they interact during certain time intervals. Consequently, predictions of effects of public health actions increasing accuracy allowing efficient preventive and corrective policies.
The COVID-19 pandemic started to emerge at the end of 2019 promoted a big interest of the whole scientific community to understand the several aspects of the epidemic using different methodologies from Mathematics and Statistical Physics.
These facts inspired the conception of the Research Topic “ - “ - “ - “
Examining these papers, it can be concluded that the contribution of this Research Topic is valuable to orient public health policies.
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