• Adaptation de la méthode basée sur le spectre de mesures à des systèmes poreux synthétiques et naturels.
• Mise au point de la version bi-dimensionnelle de la méthode de classification développée.
• Analyse de données pharmacocinétiques; stratégie globale de modélisation avec des applications spécifiques en pharmacocinétique.
• Analyse fractale: principes mathématiques et applications aux structures et signaux biologiques.

Research Interests and Objectives

My research interests focus on the use of mathematical and computational modeling to understand disease mechanisms and inform therapeutic strategies. A central theme of my work is the improvement of population pharmacokinetic (PopPK) analysis methods through the integration of modern data-driven approaches. The objective is to automate model selection, increase modeling flexibility, and improve scalability while preserving interpretability.

My research interests also include virology, ranging from HIV—particularly to study the impact of antiretroviral therapies—to Epstein–Barr virus and its role in the development of multiple sclerosis. In parallel, I am interested in immunology, with a focus on characterizing immune responses and therapeutic interventions aimed at modulating or enhancing these responses in pathological contexts.

More broadly, I seek to apply machine learning and advanced statistical methods to leverage large and complex datasets in order to improve our understanding of biological and pharmacological systems.

Expertise

I have acquired interdisciplinary expertise across multiple areas of health research. I have worked on projects in epidemiology (COVID-19), clinical epidemiology (emergency department utilization), virology (SARS-CoV-2 and HIV), immunology (immune responses to viral infection), pharmacology (population pharmacokinetics and systems pharmacology / QSP), and psychology (post-traumatic stress disorder). This breadth reflects both my scientific curiosity and my ability to adapt quantitative methods to a wide range of health-related problems.

Across all projects, I have consistently leveraged my background in mathematical and statistical modeling, as well as machine learning, to extract mechanistic insight from data.

Modeling Philosophy and Methodological Approach

The combination of mathematical modeling, data, and statistical inference theory is particularly powerful. A well-known example is population pharmacokinetic analysis. In this context, plasma drug concentration data are used to inform a mathematical model of pharmacokinetics, typically expressed as a system of differential equations. These equations describe the relationship between drug concentrations and the rates at which the drug is absorbed, distributed, and eliminated from the body.

By numerically integrating the system of equations, it is possible to generate predictions of plasma concentrations over time. When combined with a statistical error model, the framework allows for parameter estimation and model adequacy assessment through comparison with observed data. Because these models are semi-mechanistic, they can be used to extrapolate beyond observed conditions. For example, allometric relationships can be incorporated to adjust pharmacokinetic parameters and predict drug concentrations in pediatric populations based on adult data.

More generally, nearly any phenomenon can be modeled, whether it involves deterministic processes, stochastic processes (e.g., rare random events that alter system dynamics), or a combination of both. For instance, I have modeled the epidemiology of COVID-19 by studying case migration using counting processes. I have also investigated the activation of latently infected HIV-infected cells—a rare and seemingly random phenomenon—using mathematical models and particle filtering approaches (e.g., partially observed Markov processes) to estimate parameters governing stochastic dynamics.

Use of Machine Learning

I have also worked extensively with machine learning methods. In predictive settings, machine learning learns functional relationships directly from data, whereas mechanistic mathematical modeling encodes governing laws a priori. Compared to mechanistic modeling, machine learning methods often excel at interpolation but may be less interpretable and less robust outside the training domain.

I have applied machine learning techniques in a variety of contexts, including spline-based regression, random forests, neural networks (MLP, LSTM), and k-nearest neighbors regression. Given the broad applicability of machine learning, I continue to deepen my expertise in this area on an ongoing basis.