Antoine Perasso

What is the robustness of early warning signals to temporal aggregation

A number of methods have recently been developed to identify early warning signals (EWSs) within time-series structure typically characteristic of the rise of critical transitions. Inherent technical constraints often limit the possibility to obtain from sediment both regular and high-resolution time series rather most palaeoecological time series obtained from sediment records represent time-aggregated ecological signals. In this study, the robustness of EWS detection to temporal aggregation was addressed using simulated time series mimicking ecological dynamics. Using a stochastic differential equation based on a deterministic model exhibiting a critical transition between two stable equilibria, two different scenarios were simulated using different combinations of forcing and noise intensities (critical slowing-down and driver-mediated flickering scenarios). The temporal resolution of each simulated time series was progressively decreased by averaging the data from 1t = 1 up to 1t = 10 time-unit intervals. EWSs [standard deviation, autocorrelation at lag-1 (AR(1)), skewness and kurtosis] were applied to all time series. Robustness of EWSs to data aggregation was assessed through a block-based approach using Kendall rank correlation Tau. Standard deviation appeared to be robust to data aggregation up to 1t = 10 for the slowing-down scenario and up to 1t = 5 for the driver-mediated flickering scenario while autocorrelation remained robust up to 1t = 2 for the slowing-down scenario and did not support data aggregation for the driver-mediated scenario. Skewness and kurtosis performed poorly for the two scenarios and were not considered as robust EWSs even for the original simulated time series using the block-based approach. Our results suggest that high-resolution palaeoecological time series could be in a large extent suitable to support EWS analyses.

Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies

This article studies an infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination. We perform the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds, such as the basic reproduction number, that ensure extinction or persistence of the disease in the contagion process. Moreover, a numerical scheme adapted to the model is developed and analyzed. This scheme is then used to illustrate the model with numerical simulations, applying this last to the transmission of prion pathologies.

Impact of climate factors on contact rate of vector-borne diseases: Case study of malaria

Climate change influences more and more of our activities. These changes led to environmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number ℛ0 depends on the duration of transmission period and the date of the first conta-mination case that was declared (t0) in the specific case of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium (EE) and disease-free equilibrium (DFE). We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.

Identifiability problem for recovering the mortality rate in an age-structured population dynamics model

In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster–Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modelled by a non-local boundary condition, we make explicit a sufficient condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numerical simulations.

Predicting the Evolution of two Genes in the Yeast Saccharomyces Cerevisiae

Since the late ‘60s, various genome evolutionary models have been proposed to predict the evolution of a DNA sequence as the generations pass. Most of these models are based on nucleotides evolution, so they use a mutation matrix of size 4 4. They encompass for instance the well-known models of Jukes and Cantor, Kimura, and Tamura. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of a mutation matrix. To make this computation possible, particular forms for the mutation matrix are assumed, which are not compatible with mutation rates that have been recently obtained experimentally on gene ura3 of the Yeast Saccharomyces cerevisiae. Using this experimental study, authors of this paper have deduced a simple mutation matrice, compute the future evolution of the rate purine/pyrimidine for ura3, investigate the particular behavior of cytosines and thymines compared to purines, and simulate the evolution of each nucleotide.

Chaos in DNA evolution

In this paper, we explain why the chaotic model (CM) of Bahi and Michel (2008) accurately simulates gene mutations over time. First, we demonstrate that the CM model is a truly chaotic one, as defined by Devaney. Then, we show that mutations occurring in gene mutations have the same chaotic dynamic, thus making the use of chaotic models relevant for genome evolution.

Criterion of positivity for semilinear problems with applications in biology

The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.

Competence of hosts and complex foraging behavior are two cornerstones in the dynamics of trophically transmitted parasites.

Multi-host trophically transmitted parasite (TTP) is a common life cycle where prey and predators are respectively intermediate and definitive hosts of the parasite. In these systems, the foraging response of the predator toward variations in prey community composition underlies the dynamic of the parasite. Therefore, modeling epidemiological dynamic of infectious diseases considering ecological predator-prey interactions is essential to understand the spreading of parasites in ecosystems. However, two important weaknesses of previous TTP models including feeding interaction can be pointed out: (i) the choice of a linear density-dependent contact rate is faintly realistic as it supposes an unlimited ingestion rate with an increase of prey density and (ii) considering only one host prey species prevents the study of host biodiversity effect due to change in the prey community composition where species have different competences to be infected and to transmit the parasite. This article attempts to address the dynamics of parasite in a context of multiple intermediate hosts differentiated by their competences and of complex foraging behavior of the predator. We present and analyze a deterministic one predator-two prey model, which is then used to explore the transmission cycle of the cestode Echinococcus multilocularis. This study examines the foraging condition for the co-existence of the prey, and then, based on the computation of the threshold measure of disease risk, R0, we show that the pattern of feeding interactions changes the relationship between disease risk and prey community composition. Finally, we disentangle the mechanism leading to the counter-intuitive observation of a decrease of disease risk while the population density of intermediate hosts increases.

Relaxing the Hypotheses of Symmetry and Time-Reversibility in Genome Evolutionary Models

Various genome evolutionary models have been proposed these last decades to predict the evolution of a DNA sequence over time, essentially described using a mutation matrix. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of the mutation matrix. To make this computation possible, hypotheses are assumed for the matrix, such as symmetry and time-reversibility, which are not compatible with mutation rates that have been recently obtained experimentally on genes ura3 and can1 of the Yeast Saccharomyces cerevisiae. In this work, authors investigate systematically the possibility to relax either the symmetry or the time-reversibility hypothesis of the mutation matrix, by investigating all the possible matrices of size 2*2 and 3*3. As an application example, the experimental study on the Yeast Saccharomyces cerevisiae has been used in order to deduce a simple mutation matrix, and to compute the future evolution of the rate purine/pyrimidine for

Identifiability analysis of an epidemiological model in a structured population

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