Section: New Results

Miscellaneous

Participants : M. Soledad Aronna [FGV, RIo de Janeiro] , Bettina d'Avila Barros [FGV, Rio de Janeiro] , Pierre-Alexandre Bliman, Noémie Boissier, Géraldine Cellière, Flávio C. Coelho [FGV, Rio de Janeiro] , Marie Doumic, Benoît Perthame, Tales Rands Amazonas [FGV, Rio de Janeiro] , Group Reo [Inria Paris - Rocquencourt] , Edouard Ribes [SANOFI] , Martin Strugarek, Nathan Toubiana [École Polytechnique] , Paul Van Liedekerke, Nicolas Vauchelet, Jorge Zubelli [IMPA, Rio de Janeiro] .

Diffusive waves generated by a travelling wave

Observations in developmental biology show that calcic waves, generated after fertilisation within the egg cell endoplasmic reticulum, propagate within the egg cell. This motivates to explore in which circumstances a travelling wave solution of a reaction-diffusion equation can generate a travelling wave for the diffusion equation. For this purpose, we construct analytical solutions for a system composed of a reaction-diffusion equation coupled with a purely diffusive equation. We consider both the monostable (of the Fisher-KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails, the exponents of which are roots of second, third or fourth-order polynomials. These rise conditions on the coefficients for existence of a travelling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered. See [49].

Dealing with uncertainty in modelling

Interval observers for time-varying uncertain epidemiological models. SIR models constitute an elementary class of deterministic models of evolution of epidemics. We examine here the issue of state estimation for such models, subjected to seasonal variations and uncertainties in the transmission rates. Direct or indirect (through a vector) transmission is considered. In both cases, the measurement is assumed to consist of the number of new infectives per unit time, that is the information usually provided by the public health systems. We construct classes of interval observers with estimate-dependent gain, and provide corresponding asymptotic error bounds.

Modelling strategic workforce planning with structured population equations

We initiated a promising collaboration with the human resource department of Sanofi (E. Ribes), aiming at proposing a unified modelling of workforce planning based on structured population equations. Strategic Workforce Planning is a company process providing best in class, economically sound, workforce management policies and goals. Despite the abundance of literature on the subject, this is a notorious challenge in terms of implementation. Reasons span from the youth of the field itself to broader data integration concerns that arise from gathering information from financial, human resource and business excellence systems. In [43], we set the first stones to a simple yet robust quantitative framework for Strategic Workforce Planning exercises. Firstly, a method based on structured equations is detailed. It is then used to answer two main workforce-related questions: how to optimally hire to keep labour costs flat? How to build an experience-constrained workforce at a minimal cost? Further developments are in progress.