Frédéric Hamelin - Academia.edu (original) (raw)

Papers by Frédéric Hamelin

Revue Africaine de Recherche en Informatique et Mathématiques Appliquées

We use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria ... more We use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore. On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux.

arXiv (Cornell University), Mar 8, 2021

We analyze the identifiability and observability of the well-known SIR epidemic model with an add... more We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed in quarantine (SIQR model), considering that the flow of individuals placed in quarantine and the size of the quarantine population are known at any time. Then, we focus on the problem of identification of the model parameters, with the synthesis of an observer.

HAL (Le Centre pour la Communication Scientifique Directe), Jan 7, 2021

Bulletin of Mathematical Biology

Host diversification methods such as within-field mixtures (or field mosaics, depending on the sp... more Host diversification methods such as within-field mixtures (or field mosaics, depending on the spatial scale considered) are promising methods for agroecological plant disease control. We explore disease spread in host mixtures (or field mosaics) composed of two host genotypes (susceptible and resistant). The pathogen population is composed of two genotypes (wild-type and resistance-breaking). We show that for intermediate fractions of resistant hosts, the spatial spread of the disease may be split into two successive fronts. The first front is led by the wild-type pathogen and the disease spreads faster, but at a lower prevalence, than in a resistant pure stand (or landscape). The second front is led by the resistance-breaking type, which spreads slower than in a pure resistant stand (or landscape). The wild-type and the resistancebreaking genotype coexist behind the invasion fronts, resulting in the same prevalence as in a resistant pure stand. This study shows that host diversification methods may have a twofold effect on pathogen spread compared to a resistant pure stand (or landscape): on one hand they accelerate disease spread, and on the other hand they slow down the spread of the resistancebreaking genotype. This work contributes to a better understanding of the

Evolutionary Applications

It has long been recognized that sustainable agriculture requires profound changes in agricultura... more It has long been recognized that sustainable agriculture requires profound changes in agricultural practices (Eyhorn et al., 2019). Still, the vast majority of agro-ecosystems are grown as monocultures, that is, as large and continuous deployment of a single plant genotype over potentially vast areas (McDonald & Stukenbrock, 2016). The development of mechanization, plant breeding, and crop protection products promotes the use of monocultures because they facilitate crop management and ensure high yields under current management practices (Wuest et al., 2021). Unfortunately, these homogeneous and simplified agricultural landscapes are particularly vulnerable to disease outbreaks (Brown, 2015), since pathogens are best transmitted in genetically similar environments (Stukenbrock & McDonald, 2008). In addition, genetically identical crops increase the selection pressure toward pathogens overcoming plant resistance. As a result, defeated resistances are no longer of agronomic value, the available genetic diversity is eroding (Thrupp, 2000), and the need for pesticides increases (Brown & Tellier, 2011). Sustainable agriculture requires growers to preserve diversity and reduce inputs within the crops (Renard & Tilman, 2021). In

HAL (Le Centre pour la Communication Scientifique Directe), Jun 19, 2018

International audienceMany plant parasites interact with their host through gene-for-gene interac... more International audienceMany plant parasites interact with their host through gene-for-gene interactions. Considerable polymorphism for virulence (defined as the ability to overcome a resistance gene) and resistance occurs in agricultural and wild ecosystems. Fitness costs of resistance and virulence are required for polymorphism to be maintained in the long run. A previous study showed that there exist virulence costs in the Great Famine pathogen (Phytophthora infestans). These costs are mainly due to a lower spore production. However, virulent genotypes have a shorter latent period (time-to-sporulation). The latter observation is intriguing as virulent genotypes are expected to benefit from shorter latent periods. A key component of plant immunity is termed systemic acquired resistance (SAR): this is a partial resistance response that occurs following an earlier exposure to a pathogen. Through an adaptive dynamics approach, we show that SAR, by increasing the latent period of subsequent infections, may indeed select for shorter latent period in virulent genotypes. This way, we provide an original and possibly testable hypothesis to explain previously puzzling observations

Assessing life-history traits of parasites on resistant hosts is crucial in evolutionary ecology.... more Assessing life-history traits of parasites on resistant hosts is crucial in evolutionary ecology. In the particular case of sporulating pathogens with growing lesions, phenotyping is difficult because one needs to disentangle properly pathogen spread from sporulation. By considering Phytophthora infestans on potato, we use mathematical modelling to tackle this issue and refine the assessment pathogen response to quantitative host resistance. We elaborate a parsimonious leaf-scale model by convolving a lesion growth model and a sporulation function, after a latency period. This model is fitted to data obtained on two isolates inoculated on three cultivars with contrasted resistance level. Our results confirm a significant host-pathogen interaction on the various estimated traits, and a reduction of both pathogen spread and spore production, induced by host resistance. Most interestingly, we highlight that quantitative resistance also changes the sporulation function, whose mode is si...

arXiv: Dynamical Systems, 2020

In this document we introduce the concepts of Observability and Iden-tifiability in Mathematical ... more In this document we introduce the concepts of Observability and Iden-tifiability in Mathematical Epidemiology. We show that, even for simple and well known models, these properties are not always fulfilled. We also consider the problem of practical observability and identi-fiability which are connected to sensitivity and numerical condition numbers.

Saisonnalité et divergence des pathogènes hétérothalliques Castel, Mailleret, Ravigné, Hamelin De... more Saisonnalité et divergence des pathogènes hétérothalliques Castel, Mailleret, Ravigné, Hamelin Deux modes : homothallique hétérothallique c Julie Clément, P. infestans Implications en termes écologiques : effet Allee, capacité d'invasion évolutifs :émergence et maintien de la diversité Saisonnalité et divergence des pathogènes hétérothalliques Castel, Mailleret, Ravigné, Hamelin Saisonnalité et divergence des pathogènes hétérothalliques Castel, Mailleret, Ravigné, Hamelin Saisonnalité et divergence des pathogènes hétérothalliques Castel, Mailleret, Ravigné, Hamelin

To date, relatively few studies have focused on the effects of sex on population dynamics. Previo... more To date, relatively few studies have focused on the effects of sex on population dynamics. Previous models found that sexual reproduction may either dampen population fluctuations or accentuate population fluctuations, depending on mating system notably. Here we were interested in the effect of mate limitation in pathogens in which both sexual and asexual reproductions occur simultaneously within direct life cycles, a life history typical of many fungal plant pathogens for instance. We modelled the epidemiological dynamics of such species by considering a SIR model with two modes of transmission, one linear and the other bilinear in infected density. We found that the threshold for epidemic development is the same as expected under strictly asexual dynamics. We showed that sexual spore production promotes more complex dynamics (cycles) than strictly asexual reproduction. We further showed that sexual reproduction has important consequences for the coexistence of parasites infecting ...

2019 American Control Conference (ACC), 2019

This paper presents a new methodology for distributed model predictive control of large-scale sys... more This paper presents a new methodology for distributed model predictive control of large-scale systems. The methodology involves two distinct stages, i.e., the decomposition of large-scale systems into subsystems and the design of subsystem controllers. Two procedures are used: in the first stage, the structure of the Karush-Kuhn-Tucker matrix resulting from the necessary optimality conditions is exploited to yield a decomposition of the large-scale system into several subsystems. In the second stage, a particular technique, the socalled optimality condition decomposition makes it possible to synthesize distributed coordinated subcontrollers thus achieving an optimal distributed control of the large-scale system. The convergence of the proposed approach is stated.

Quadrature, 2021

On etudie une epidemie modelisee par un systeme differentiel de type S-I-R ou S-E-I-R. Pour le mo... more On etudie une epidemie modelisee par un systeme differentiel de type S-I-R ou S-E-I-R. Pour le modele S-I-R, on montre que la date du pic epidemique n'est pas toujours une fonction decroissante du taux de contact. Pour le modele S-E-I-R, lorsque la population N est grande, de nouveaux elements tendent a confirmer la conjecture selon laquelle le pic epidemique a lieu au temps T, avec T∼(ln⁡N)/λ , ou λ est la plus grande valeur propre du systeme linearise.

Proceedings of the 6th International Conference on Smart Cities and Green ICT Systems, 2017

This paper deals with the problem of modelling and controlling a multi-zone office building to en... more This paper deals with the problem of modelling and controlling a multi-zone office building to ensure its thermal comfort by an optimal and cost effective management of the energy consumption. A thermal behaviour analysis of the building is carried out using the Simscape TM library in MATLAB/Simulink R environment that leads to a multi-model representation. Based on this modelling, the Yalmip toolbox in the MATLAB programming environment or an iterative optimization algorithm can be used to solve the control optimisation problem. The design of a model predictive control associated with a wise choice of the cost function makes it possible to obtain in simulation substantial energy benefits.

ABSTRACTMany plant viruses are transmitted by insect vectors. Transmission can be described as pe... more ABSTRACTMany plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector’s own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding – as well as potential effects of infection on vector population density – on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this ...

Bulletin of Mathematical Biology, 2021

The distribution and use of pathogen-free planting material ("clean seeds") is a promising method... more The distribution and use of pathogen-free planting material ("clean seeds") is a promising method to control plant diseases in developing countries. We address the question of minimizing disease prevalence in plants through the optimal usage of clean seeds. We consider the simplest possible S-I model together with a simple economic criterion to be maximized. The static optimization problem shows a diversity of possible outcomes depending on economical and epidemiological parameters. We derive a simple condition showing to what extent subsidizing clean seeds relative to the epidemiological features of the disease may help eradicate or control the disease. Then we consider dynamic optimal control and Pontryagin's maximum principle to study the optimal usage of clean seeds to control the disease. The dynamical results are comparable to the static ones and are even simpler in some sense. In particular, the condition on the critical subsidy rate that makes clean seed usage economically viable is unchanged from the static optimization case. We discuss how these results may apply to the control of maize lethal necrosis (MLN) in East-Africa. 1 Introduction Plant diseases cause economic devastation especially in developing countries by severely affecting production of staple food crops due to yield losses. Cassava

Phytopathology®, 2020

Host mixtures are a promising method for agroecological plant disease control. Plant immunity is ... more Host mixtures are a promising method for agroecological plant disease control. Plant immunity is key to the success of host mixtures against polymorphic pathogen populations. This immunity results from priming-induced cross-protection, whereby plants able to resist infection by specific pathogen genotypes become more resistant to other pathogen genotypes. Strikingly, this phenomenon was absent from mathematical models aiming at designing host mixtures. We developed a model to specifically explore how priming affects the coexistence of two pathogen genotypes in host mixtures composed of two host genotypes and how it affects disease prevalence. The main effect of priming is to reduce the coexistence region in the parameter space (due to the cross-protection) and to generate a singular mixture of resistant and susceptible hosts corresponding to the maximal reduction disease prevalence (in absence of priming, a resistant pure stand is optimal). The epidemiological advantage of host mixt...

Viruses, 2019

Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural pl... more Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural plant communities. A variety of models have been used to investigate the dynamics of co-infection which track only the disease status of infected and co-infected plants, and which do not explicitly track the density of inoculative vectors. Much less attention has been paid to the role of vector transmission in co-infection, that is, acquisition and inoculation and their synergistic and antagonistic interactions. In this investigation, a general epidemiological model is formulated for one vector species and one plant species with potential co-infection in the host plant by two viruses. The basic reproduction number provides conditions for successful invasion of a single virus. We derive a new invasion threshold which provides conditions for successful invasion of a second virus. These two thresholds highlight some key epidemiological parameters important in vector transmission. To illustrat...

If pathogen species, strains or clones do not interact, intuition suggests the proportion of co-i... more If pathogen species, strains or clones do not interact, intuition suggests the proportion of co-infected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of co-infected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of co-infected hosts is expected to be higher than multiplication would suggest. By modeling the dynamics of multiple non-interacting pathogens, we develop a pair of novel tests of interaction that properly account for non-independence. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates ...