Genomic surveillance of SARS-CoV-2 Spike gene by sanger sequencing.

The SARS-CoV-2 responsible for the ongoing COVID pandemic reveals particular evolutionary dynamics and an extensive polymorphism, mainly in Spike gene. Monitoring the S gene mutations is crucial for successful controlling measures and detecting variants that can evade vaccine immunity. Even after the costs reduction resulting from the pandemic, the new generation sequencing methodologies remain unavailable to a large number of scientific groups.

N-body dynamics on closed surfaces: the axioms of mechanics.

A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces endowed with a metric .

Epidemics Modelings: Some New Challenges.

Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathematical modeling is used in particular to reach a better understanding of some neglected diseases (dengue, malaria, …) and of new emerging ones (SARS, influenza A,….) of big agglomerates.

Point-vortex cluster formation in the plane and on the sphere: an energy bifurcation condition.

The dynamics of a system of point vortices is considered in the plane and on the sphere. Particular attention is given to the formation of vortex clusters and to global vortex dynamics, especially in the spherical case. For integrable systems and systems with given symmetries, we show the existence of a critical energy above or below which (depending on the geometry of the surface) the system splits into clusters and vortex dynamics is confined to a particular region.