We focus on population dynamics, usually of host-natural enemy interactions, to understand fundamental processes in epidemiology, ecology and evolution of infectious disease. Our works are based on a combination of Mathematical analysis and Modeling with a particular focus on Dynamical Systems.

## Population dynamics

By involving many fields (mathematics, social sciences, biology), the aim here is to describe variations over time of biological systems. These systems involve a time variable and one or more structuring variables (time since infection, chronological age, space, phenotypic trait, etc.). In a deterministic framework, these systems are usually described by ODEs (Ordinary Differential Equations), DDEs (Delayed Differential Equations) or PDEs (Partial Derivative Equations). Their study is based on dynamical systems theory.

## Scientific computing

Quite often, a very high complexity (i.e., too strong nonlinearity) of the modeling problem leads to situations where it is difficult to conduct a complete mathematical analysis of the model dynamics. In such cases, it is useful to be able to use the techniques of scientific calculation. It is a discipline that allows a complete numerical experimentation of the model by bringing together a set of mathematical and computer science tools.

## Antimicrobial resistance

Defining sustainable strategies for managing antimicrobial efficiency (a worldwide major problem), in space and time, by considering the continuous character of antimicrobial resistance with varying degrees of intermediate resistance (called tolerance).

## Durability of plant disease resistance genes

Plants disease resistance genes are not eternal and mathematical models can lead to practical insights on the optimal deployment in time and space to sustainably manage varietal resistance in agro-ecosystems.

## Adaptive dynamics

We study evolutionary dynamics of a population, for e.g., by taking into account mutation or selection processes. Here, a focus is on integro-differential equations with nonlocal terms.

## Human malaria

The host-vector pairing is a fundamental relationship in the transmission and evolution of malaria parasites. Through the bacterial diversity within a host, different parasitic forms and environmental impact on the evolution of the vector, we develop models at both within- and between-host scales to better understand mechanisms favouring the persistence of this disease.

## Optimal control of infectious diseases

Management or control of an outbreak is a priority for both public health concerns and environmental considerations. Optimal control theory is a tremendous means for studying and proposing decision support tools. We develop works around this theory for infectious diseases such as COVID-19, HIV or HBV.