Quentin Richard

• PhD
• Assistant Professor at Université de Montpellier

Malaria poses a significant global health challenge, with millions of cases and fatalities reported annually, primarily in the WHO African Region and SouthEast Asia Region. Mixed-species malaria infections are common but often underestimated, even in regions with low transmission rates. Mathematical models have been instrumental in studying parasit...

Host age variation is a striking source of heterogeneity that can shape the evolution and transmission dynamic of pathogens. Compared with vertebrate systems, our understanding of the impact of host age on invertebrate–pathogen interactions remains limited. We examined the influence of mosquito age on key life-history traits driving human malaria t...

Host age variation is a striking source of heterogeneity that can shape the evolution and transmission dynamic of pathogens. Compared to vertebrate systems, our understanding of the impact of host age on invertebrate-pathogen interactions remains limited. We examined the influence of mosquito age on key life-history traits driving human malaria tra...

The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time a...

Malaria is one of the most common mosquito-borne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. Few models considering a multiple structure model formulation including (i) the chronological age of human and mosquito populations, (ii) the time since they are infected, and (iii) humans wa...

We have modeled the evolutionary epidemiology of spore‐producing plant pathogens in heterogeneous environments sown with several cultivars carrying quantitative resistances. The model explicitly tracks the infection‐age structure and genetic composition of the pathogen population. Each strain is characterized by pathogenicity traits determining its...

The Covid-19 pandemic outbreak was followed by an huge amount of modeling studies in order to rapidly gain insights to implement the best public health policies. However, most of those compartmental models used a classical ordinary differential equations (ODEs) system based formalism that came with the tacit assumption the time spent in each compar...

In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. W...

In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes population, (ii) the time since humans and mosquitoes are infected and (iii) humans waning immunity (i.e., the progres...

In this work we consider a nonlocal system modelling the evolutionary adaptation of a pathogen within a multi-host population of plants. Here we focus our analysis on the study of the stationary states. We first discuss the existence of nontrivial equilibria using dynamical system arguments. Then we introduce a small parameter 0<ε≪1 that characteri...

In this work, we consider a reaction–diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. Using a semigroup approach in , we prove global existence, uniqueness, and positivity of the solutions. The nonlinearity is handled by providing estimates in , allowing to deal with most of the functional responses that...

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov...

This work provides a general spectral analysis of size-structured two-phase population models. Systematic functional analytic results are given. We deal first with the case of finite maximal size. We characterize the irreducibility of the corresponding $L^{1}$ semigroup in terms of properties of the different parameters of the system. We characteri...

In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been infected for. The latter allows to take into account the variation of infectiousness as a function of time since infection. In the absence of pharmaceutical interventions such as a vaccine o...

We study a competitive infection-age structured SI model between two diseases. The well- posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number $R_0^x$ and $R_0^y$ of each strain. We then exhibit Lya...

In this work we consider an epidemic system modelling the evolution of a spore-producing pathogen within a multi-host population of plants. Here we focus our analysis on the study of the stationary states. We first discuss the existence of such nontrivial states by using the theory of global attractors. Then we introduce a small parameter epsilon t...

We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number $R_0^x$ and $R_0^y$ of each strain. We then exhibit Lyap...

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov...

This work provides a general spectral analysis of size-structured two-phase population models. Systematic functional analytic results are given. We deal first with the case of finite maximal size. We characterize the irreducibility of the corresponding $L^{1}$ semigroup in terms of properties of the different parameters of the system. We characteri...

In this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplanktons and zooplanktons. Using a semigroup approach in $L^2$, we prove global existence, uniqueness and positivity of the solutions. The Holling type 2 nonlinearities, i.e of rational type with singularity, are handled by providing estimates i...

In this article, we study the behavior of a nonlinear age-structured predator-prey model that is a generalization of Lotka-Volterra equations. We prove global existence, uniqueness and positivity of the solution using a semigroup approach. We make some analytically explicit thresholds that ensure, or not depending of their values, the boundedness o...

This work revisits and extends in various directions a work by J.Z. Farkas and P. Hinow (Math. Biosc and Eng, 8 (2011) 503-513) on structured populations models (with bounded sizes) with diffusion and generalized Wentzell boundary conditions. In particular, we provide first a self-contained L¹ generation theory making explicit the domain of the gen...

In this thesis we look at some structured populations models described with transport equations. The well-posedness and the positivity of the solutions are systematically shown in the semigroups setting in a L1 framework. A first work is dedicated to a age-structured predator/prey system. A stability study of the equilibria allow us to give explici...

This thesis is dedicated to some structured populations models described with transport or transport-diffusion equations. The well-posedness, in the semigroupes setting in L1 and the positivity of the solutions are systematically shown. A first work is dedicated to an age-structured predator/prey system. A stability study of the equilibria allow us...