arXiv subjects

Elisabeta Vergu

Publications and source records attributed to Elisabeta Vergu.

9 recordsLinked to original sources

arXiv2025

The contact process on Scale-Free Percolation

We consider the contact process on scale-free percolation, a spatial random graph model where the degree distribution of the vertices follows a power law with exponent $β$. We study the extinction time $τ_{G_n}$ of the contact process on the graph restricted to a d-dimensional box of volume n, starting from full occupancy. In the regime $β\in (2, 3)$, where the degrees have finite mean but infinite variance and the graph exhibits the ultra-small world behaviour, we adapt the techniques of [Linker et al., 2021] to show that $τ_{G_n}$ is exponential in n. Our main contribution, though, deals with the case $β\geq 3$, where the degrees have finite variance and the graph is small-world. We prove that also in this case $τ_{G_n}$ grows exponentially, at least up to a logarithmic correction reflecting the sparser graph structure. The proof requires the generalization of a result from [Mountford et al., 2016] and combines a multi-scale analysis of the graph, the study of the chemical distance between vertices and percolation arguments.

math.PR↗

arXiv2024

The epidemiological footprint of contact structures in models with two levels of mixing

Models with several levels of mixing (households, workplaces), as well as various corresponding formulations for R0, have been proposed in the literature. However, little attention has been paid to the impact of the distribution of the population size within social structures, effect that can help plan effective interventions. We focus on the influence on the model outcomes of teleworking strategies, consisting in reshaping the distribution of workplace sizes. We consider a stochastic SIR model with two levels of mixing, accounting for a uniformly mixing general population, each individual belonging also to a household and a workplace. The variance of the workplace size distribution appears to be a good proxy for the impact of this distribution on key outcomes of the epidemic, such as epidemic size and peak. In particular, our findings suggest that strategies where the proportion of individuals teleworking depends sublinearly on the size of the workplace outperform the strategy with linear dependence. Besides, one drawback of the model with multiple levels of mixing is its complexity, raising interest in a reduced model. We propose a homogeneously mixing SIR ODE-based model, whose infection rate is chosen as to observe the growth rate of the initial model. This reduced model yields a generally satisfying approximation of the epidemic. These results, robust to various changes in model structure, are very promising from the perspective of implementing effective strategies based on social distancing of specific contacts. Furthermore, they contribute to the effort of building relevant approximations of individual based models at intermediate scales.

physics.soc-ph↗

arXiv2024

Performing global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology

In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology. Our goal is to quantify not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments), but also those of intrinsic randomness and interactions between epidemic parameters and intrinsic randomness. For that purpose, following what was proposed in Navarro Jimenez et al, we leverage three exact simulation algorithms for continuous-time Markov chains from the state of the art which we combine with common tools from variance-based sensitivity analysis as introduced in Sobol (1993). Also, we discuss the impact of the choice of the simulation algorithm used for the simulations on the results of sensitivity analysis. Such a discussion is new, at least to our knowledge. In a numerical section, we implement and compare three sensitivity analyses based on simulations obtained from different exact simulation algorithms of a SARS-CoV-2 epidemic model.

stat.ME↗

arXiv2023

Inference using a composite-likelihood approximation for stochastic metapopulation model of disease spread

Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to complex stochastic models. Such complexity together with data characteristics make the analysis of these systems a challenge. Our objective was to develop a new inference procedure to estimate key parameters of stochastic metapopulation models of animal disease spread from longitudinal and spatial datasets, while accurately accounting for characteristics of census data. We applied our procedure to provide new knowledge on the regional spread of \emph{Mycobacterium avium} subsp. \emph{paratuberculosis} (\emph{Map}), which causes bovine paratuberculosis, a worldwide endemic disease. \emph{Map} spread between herds through trade movements was modeled with a stochastic mechanistic model. Comprehensive data from 2005 to 2013 on cattle movements in 12,857 dairy herds in Brittany (western France) and partial data on animal infection status in 2,278 herds sampled from 2007 to 2013 were used. Inference was performed using a new criterion based on a Monte-Carlo approximation of a composite likelihood, coupled to a numerical optimization algorithm (Nelder-Mead Simplex-like). Our criterion showed a clear superiority to alternative ones in identifying the right parameter values, as assessed by an empirical identifiability on simulated data. Point estimates and profile likelihoods allowed us to establish the initial state of the system, identify the risk of pathogen introduction from outside the metapopulation, and confirm the assumption of the low sensitivity of the diagnostic test. Our inference procedure could easily be applied to other spatio-temporal infection dynamics, especially when ABC-like methods face challenges in defining relevant summary statistics.

q-bio.PE↗

arXiv2021

Inference in Gaussian state-space models with mixed effects for multiple epidemic dynamics

The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different periods. The resulting possible inter-epidemic variability is rarely explicitly considered. Here, we propose to tackle multiple epidemics through a unique model incorporating a stochastic representation for each epidemic and to jointly estimate its parameters from noisy and partial observations. By building on a previous work, a Gaussian state-space model is extended to a model with mixed effects on the parameters describing simultaneously several epidemics and their observation process. An appropriate inference method is developed, by coupling the SAEM algorithm with Kalman-type filtering. Its performances are investigated on SIR simulated data. Our method outperforms an inference method separately processing each dataset. An application to SEIR influenza outbreaks in France over several years using incidence data is also carried out, by proposing a new version of the filtering algorithm. Parameter estimations highlight a non-negligible variability between influenza seasons, both in transmission and case reporting. The main contribution of our study is to rigorously and explicitly account for the inter-epidemic variability between multiple outbreaks, both from the viewpoint of modeling and inference.

stat.ME↗

arXiv2021

Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data and calibration of numerous tuning parameters. In particular, as coordinates of dynamic epidemic models are coupled, the presence of unobserved coordinates leads to a statistically difficult problem. The aim is to propose an easy-to-use and general inference method that is able to tackle these issues. First, using the properties of epidemics in large populations, a two-layer model is constructed. Via a diffusion-based approach, a Gaussian approximation of the epidemic density-dependent Markovian jump process is obtained, representing the state model. The observational model, consisting of noisy observations of certain model coordinates, is approximated by Gaussian distributions. Then, an inference method based on an approximate likelihood using Kalman filtering recursion is developed to estimate parameters of both the state and observational models. The performance of estimators of key model parameters is assessed on simulated data of SIR epidemic dynamics for different scenarios with respect to the population size and the number of observations. This performance is compared with that obtained using the well-known maximum iterated filtering method. Finally, the inference method is applied to a real data set on an influenza outbreak in a British boarding school in 1978.

stat.AP↗

arXiv2013

Approximation of epidemic models by diffusion processes and their statistical inference

Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating $(Z(t))$. First, \previous results on the approximation of density-dependent $SIR$-like models by diffusion processes with small diffusion coefficient $\frac{1}{\sqrt{N}}$, where $N$ is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number $n$ of observations, which corresponds to the epidemic context, and for $N\rightarrow \infty$. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as $R_0$ (the basic reproduction number), $N$, $n$ are investigated on simulations. Two models, $SIR$ and $SIRS$, corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

stat.ME↗

arXiv2013

Epidemics in markets with trade friction and imperfect transactions

Market trade-routes can support infectious-disease transmission, impacting biological populations and even disrupting causal trade. Epidemiological models increasingly account for reductions in infectious contact, such as risk-aversion behaviour in response to pathogen outbreaks. However, market dynamics clearly differ from simple risk-aversion, as are driven by different motivation and conditioned by trade constraints, known in economics as friction, that arise because exchanges are costly. Here we develop a novel economic-market model where transient and long-term market dynamics are determined by trade friction and agent adaptation, and can influence disease transmission. We specify the participants, frequency, volume, and price in trade transactions, and investigate, using analytical insights and simulation, how trade friction affects joint market and epidemiological dynamics. The friction values explored encompass estimates from French cattle and pig markets. We show that, when trade is the dominant route of transmission, market friction can be a significantly stronger determinant of epidemics than risk-aversion behaviour. In particular, there is a critical friction level above which epidemics do not occur. For a given level of friction, open unregulated markets can boost epidemics compared with closed or tightly regulated markets. Our results are robust to model specificities and can hold in the presence of non-trade disease-transmission routes. In particular, we try to explain why outbreaks in French livestock markets appear more frequently in cattle than swine despite swine trade-flow being larger. To minimize contagion in markets, safety policies could generate incentives for larger-volume, less-frequent transactions, increasing trade friction without necessarily affecting overall trade flow.

q-bio.PE↗

arXiv2013

Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b(α,X(t)) and diffusion coefficient εσ(β,X(t)). The diffusion is discretely observed at times t_k=kΔ for k=1..n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ε. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ε\rightarrow0 and of (α,β) for Δ\rightarrow0 and ε\rightarrow0. We compare the estimators obtained with various methods and for various magnitudes of Δ and ε based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.

math.ST↗