Stability of Piecewise Deterministic Markovian Metapopulation Processes on Networks

The purpose of this paper is to study a Markovian metapopulation model on a directed graph with edge-supported transfers and deterministic intra-nodal population dynamics. We first state tractable stability conditions for two typical frameworks motivated by applications: constant jump rates with multiplicative transfer amplitudes, and coercive jump rates with unitary transfers. More general criteria for boundedness, petiteness and ergodicity are then given

RBCS1 expression in coffee: Coffea orthologs, Coffea arabica homeologs, and expression variability between genotypes and under drought stress

Background: In higher plants, the inhibition of photosynthetic capacity under drought is attributable to stomatal and non-stomatal (i.e., photochemical and biochemical) effects. In particular, a disruption of photosynthetic metabolism and Rubisco regulation can be observed. Several studies reported reduced expression of the RBCS genes, which encode the Rubisco small subunit, under water stress. Results: Expression of the RBCS1 gene was analysed in the allopolyploid context of C. arabica, which originates from a natural cross between the C. canephora and C. eugenioides species. Our study revealed the existence of two homeologous RBCS1 genes in C. arabica: one carried by the C. canephora sub-genome (called CaCc) and the other carried by the C. eugenioides sub-genome (called CaCe). Using specific primer pairs for each homeolog, expression studies revealed that CaCe was expressed in C. eugenioides and C. arabica but was undetectable in C. canephora. On the other hand, CaCc was expressed in C. canephora but almost completely silenced in non-introgressed ("pure") genotypes of C. arabica. However, enhanced CaCc expression was observed in most C. arabica cultivars with introgressed C. canephora genome. In addition, total RBCS1 expression was higher for C. arabica cultivars that had recently introgressed C. canephora genome than for "pure" cultivars. For both species, water stress led to an important decrease in the abundance of RBCS1 transcripts. This was observed for plants grown in either greenhouse or field conditions under severe or moderate drought. However, this reduction of RBCS1 gene expression was not accompanied by a decrease in the corresponding protein in the leaves of C. canephora subjected to water withdrawal. In that case, the amount of RBCS1 was even higher under drought than under unstressed (irrigated) conditions, which suggests great stability of RBCS1 under adverse water conditions. On the other hand, for C. arabica, high nocturnal expression of RBCS1 could also explain the accumulation of the RBCS1 protein under water stress. Altogether, the results presented here suggest that the content of RBCS was not responsible for the loss of photosynthetic capacity that is commonly observed in water-stressed coffee plants. Conclusion: We showed that the CaCe homeolog was expressed in C. eugenioides and non-introgressed ("pure") genotypes of C. arabica but that it was undetectable in C. canephora. On the other hand, the CaCc homeolog was expressed in C. canephora but highly repressed in C. arabica. Expression of the CaCc homeolog was enhanced in C. arabica cultivars that experienced recent introgression with C. canephora. For both C. canephora and C. arabica species, total RBCS1 gene expression was highly reduced with WS. Unexpectedly, the accumulation of RBCS1 protein was observed in the leaves of C. canephora under WS, possibly coming from nocturnal RBCS1 expression. These results suggest that the increase in the amount of RBCS1 protein could contribute to the antioxidative function of photorespiration in water-stressed coffee plants. (Résumé d'auteur

Population dynamics and epidemic processes on a trade network

On s’intéresse à la modélisation mathématique de dynamiques de populations sur des réseaux d’échange de bovins couplées avec des processus épidémiques.On discute tout d’abord de modèles de métapopulations prenant en compte des dynamiques démographiques locales (immigration, naissances, morts et mouvements d’animaux dus aux échanges entre les nœuds du réseau). Des critères de stabilité sont établis pour des modèles markoviens dans lesquels les dynamiques locales sont déterministes et les transferts entre nœuds sont stochastiques, pour un processus de branchement multitype avec immigration et pour un processus de sauts à espace d'états finis à taux logistiques. Dans les deux derniers cas, on étudie les limites d'échelle des processus en temps fini ainsi que leur stabilité sur des échelles de temps exprimées comme fonctions exponentielles du paramètre d'échelle.Dans une deuxième partie, on réalise un couplage des modèles de sauts considérés avec un processus épidémique SIR (Susceptible --- Infecté --- Rétabli), rendant compte de contacts infectieux locaux et de la propagation d’un pathogène dans le réseau au gré des mouvements d’animaux entre les nœuds. On établit une approximation du processus épidémique par un processus de branchement multitype sur des intervalles de temps fini, puis l'on fournit une méthode de calcul approché de la probabilité d'un épisode épidémique majeur, défini comme l'événement de survie du branchement approchant. On montre ensuite que dans le cas d’un événement épidémique majeur et sous contrainte de stabilité d’un équilibre endémique pour un système déterministe associé, le temps d’extinction de l’épidémie et sa taille totale évoluent de façon au moins exponentielle par rapport au paramètre d’échelle du modèle.On effectue enfin une application numérique des résultats théoriques obtenus sur le modèle SIR couplé avec des dynamiques de population logistiques. On calibre les paramètres démographiques de ce modèle sur le réseau d’échanges de bovins du Finistère observé sur l’année 2015, puis l'on calcule plusieurs indicateurs de la vulnérabilité du réseau induite par les différentes exploitations. Une procédure est détaillée afin de comparer l'efficacité relative de trois types de stratégies de contrôle (dépistage à l’importation, isolation et vaccination) ciblant les exploitations identifiées comme critiques vis-à-vis des indicateurs calculés.This thesis discusses the mathematical modelling of population dynamics on cattle trade networks coupled with epidemic processes.We first consider metapopulation models taking into account local demographic dynamics (immigration, births, deaths and animal movements due to trade between the nodes of the network). Recurrence and ergodicity criteria are stated for Markovian models with deterministic local dynamics and stochastic inter-nodal transferts, for a multitype branching process with immigration and for a jump process with logistic rates on a finite state space. In these last two cases, we study scaling limits of processes over finite time intervals and their stability over time scales that are exponentials of the scaling parameter.In a second part, we define a coupling of the jump population models considered with an SIR (Susceptible --- Infected --- Removed) epidemic dynamics. The resulting process accounts for local infectious contacts and pathogen propagation on the network due to movements of infective animals. We approximate the epidemic process by a multitype branching process on finite time intervals, then provide an iterative method to compute the probability of a emph{major epidemic outbreak}, defined as the event of survival of the approximating branching process. We then show that conditionally on a major epidemic outbreak and under a stability condition for an endemic equilibrium of the associated dynamical system, the extinction time and final size of the epidemic grow at least exponentially with respect to the scaling parameter of the model.We finally perform a numerical application of the theoretical results obtained on the SIR model coupled with logistic population dynamics. Calibrating the demographical model parameters on the 2015 Finistère cattle trade network, we compute indicators of the epidemic vulnerability of the network induced by individual holdings. We detail a protocol to assess the relative efficiency of three types of control strategies (screening at importation, isolation and vaccination) targeting the holdings identified as critical for the computed indicators

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

International audienceWe define and study an open stochastic SIR (Susceptible-Infected-Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Population transition intensities are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock farming region in western France (Finistere) and epidemiological parameters corresponding to an infectious epizootic disease. Then we exhibit an exponential lower bound for the extinction time and the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using results inspired by the Freidlin-Wentzell theory of large deviations from a dynamical system