Bouchra Nasri

We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility models and regime‐switching models with possibly zero‐inflated regimes. The main novelty of this article is to be able to test for conditional independence between several time series with arbitrary distributions, extending previous results of Duchesne, Ghoudi, and Rémillard (2012), obtained only for stochastic volatility models. We define families of empirical processes constructed from lagged generalized errors, and we show that their joint asymptotic distributions are Gaussian and independent of the estimated parameters of the individual time series. Möbius transformations of the empirical processes are used to obtain tractable covariances. Several tests statistics are then proposed, based on Cramér–von Mises type statistics and dependence measures, as well as graphical methods to visualize the dependence. In addition, numerical experiments are performed to assess the power of the proposed tests. Finally, to show the usefulness of our methodologies, examples of applications for financial data and crime data are given to cover both discrete and continuous cases. All developed methodologies are implemented in the CRAN package IndGenErrors (Ghoudi et al., 2025).

Background: Highly pathogenic avian influenza (HPAI) viruses, particularly subtypes such as H5N1 and H7N9, have caused widespread outbreaks in wild birds, poultry, livestock and occasionally humans, raising concerns about cross-species transmission and pandemic potential. Effective control and surveillance strategies require a thorough understanding of HPAI transmission dynamics, which can be supported by mathematical modelling. Objective: This scoping review aimed to identify mechanistic models used to study HPAI transmission. Specifically, we sought to categorize model types, describe their application contexts (e.g., wild birds, poultry, livestock, and humans), and highlight modelling gaps relevant to understanding and mitigating the risks of HPAI spread. Methods: Following PRISMA guidelines and the PRISMA extension for scoping reviews (PRISMA-ScR), we conducted systematic searches of PubMed and Web of Science to identify peer-reviewed studies employing deterministic and stochastic models to analyze HPAI transmission. Eligible articles published between January 2023 and June 2025 were screened and grouped by model structure, host populations, transmission pathways, and modelling objectives. Results: After screening, 30 studies published after 2023 were included in this scoping review. Compartmental models were the most common (26 studies), with 16 deterministic and 10 stochastic approaches. These models were primarily used to describe transmission among wild birds, poultry, livestock, and humans and to evaluate interventions such as culling, vaccination, and movement restrictions. Agent-based models (2 studies) captured individual-level interactions and spatial heterogeneity, while network models (2 studies) represented contact structures and transmission pathways between farms or species. Conclusions: Currently, mechanistic modelling of HPAI is dominated by compartmental approaches, including both deterministic and stochastic formulations, whereas agent-based and network models remain relatively underused. Although most studies focus on transmission in wild birds and poultry, and in some cases spillover infections to humans, few explicitly examine infection dynamics in livestock or in transmission between livestock and humans, despite the importance of livestock (e.g., cattle) as potential intermediaries in human infection. Key gaps persist in the integration of empirical data, representation of multi-host interactions, and evaluation of realistic intervention strategies. Addressing these limitations is essential to improve predictive accuracy and to strengthen the role of modelling in informing HPAI surveillance and control.

We develop a self contained stochastic perturbation theory for discrete generation and multivariate Ensemble Kalman filters. Unlike their continuous-time counterparts, discrete EnKF algorithms are defined through a two steps prediction update mechanism and exhibit non Gaussian fluctuations, even in linear settings. In the multivariate case, these fluctuations take the form of non central Wishart type perturbations, which significantly complicate the mathematical analysis. We establish non asymptotic, time-uniform stability and error estimates for the ensemble covariance matrix processes under minimal structural assumptions on the signal observation model, allowing for possibly unstable dynamics. Our results quantify the impact of ensemble size, dimension, and observation noise, and provide explicit bounds on the propagation of stochastic errors over long time horizons. The analysis relies on a detailed study of stochastic Riccati difference equations driven by matrix-valued noncentral Wishart fluctuations. Beyond their relevance to data assimilation, these results contribute to the probabilistic understanding of ensemble-based filtering methods in high dimension and offer new tools for the analysis of interacting particle systems with matrix-valued dynamics.

Background: The dynamics of HIV and ZIKV coinfection among pregnant women remain understudied, and its impacts on neonatal health still need to be defined. This gap is particularly concerning given the significant public health risks it can cause, especially in Latin America and the Caribbean, where the Zika virus is still circulating. Methods: We conducted a transversal ecological study using aggregated data from 2015 to 2023. To do so, we developed a compartmental model that included a Susceptible-Infected-Recovered (SIR) compartment for pregnant women related to HIV and ZIKV infection status, as well as SI compartments for their newborns and ZIKV-carrying mosquitoes to perform simulations representing different epidemiological scenarios. We calculated the HIV/ZIKV basic reproduction number R0. Sensitivity analysis was performed to identify the model parameter with the greatest impact on this metric. Finally, we applied personal and sexual protection, medical treatment for Zika, and antiretroviral therapy as control measures against viral infections to evaluate the most effective strategy to improve neonatal health outcomes. Results: The basic reproduction number ℛ ₀ associated with HIV/ZIKV coinfection among pregnant women varied in the range [0.09, 1.29] in the countries studied. The sensitivity analysis revealed that the ℛ ₀ was most sensitive to the mosquito biting rate and the pregnant women’s death rate. ZIKV infection rate among pregnant women had a greater impact on the number of newborns with related health problems compared to HIV infection rate. The introduction of ZIKV among pregnant women was enough to cause a surge in the number of newborns with related health issues, demonstrating a greater impact than HIV on neonatal health. When control strategies were applied to the model, simulations demonstrated that their application needed to be maintained concurrently over time and that medical treatment of Zika was the measure having the least influence on the coinfection. Conclusion: Since pregnant women infected with HIV are particularly vulnerable to other infections such as ZIKV, it is crucial to improve antenatal care among them. Continued monitoring and increased prevention of HIV sexual transmission is also necessary to ensure maternal and child health. In order to optimize public health interventions, it is important to extend the research to strengthen our understanding of the implications of HIV-ZIKV coinfection among pregnant women and its effects on their children.

In this article, we study sequential change-point methods for discretely observed generalized Ornstein-Uhlenbeck processes with periodic drift. Two detection methods are proposed, and their respective performance is studied through numerical experiments for several choices of parameters.

Zika virus (ZIKV) infection, along with the concurrent circulation of other arboviruses, presents a great public health challenge, reminding the utilization of mathematical modelling as a crucial tool for explaining its intricate dynamics and interactions with co-circulating pathogens. Through a scoping review, we aimed to discern current mathematical models investigating ZIKV dynamics, focusing on its interplay with other pathogens, and to identify underlying assumptions and deficiencies supporting attention, particularly regarding the epidemiological attributes characterizing Zika outbreaks. Following the PRISMA-Sc guidelines, a systematic search across PubMed, Web of Science, and MathSciNet provided 137 pertinent studies from an initial pool of 2446 papers, showing a diversity of modelling approaches, predominantly centered on vector-host compartmental models, with a notable concentration on the epidemiological landscapes of Colombia and Brazil during the 2015–2016 Zika epidemic. While modelling studies have been important in explaining Zika transmission dynamics and their intersections with diseases such as Dengue, Chikungunya, and COVID-19 so far, future Zika models should prioritize robust data integration and rigorous validation against diverse datasets to improve the accuracy and reliability of epidemic prediction. In addition, models could benefit from adaptable frameworks incorporating human behavior, environmental factors, and stochastic parameters, with an emphasis on open-access tools to foster transparency and research collaboration.

This paper presents a mathematical model to investigate the co-infection with human immunodeficiency virus (HIV) and Zika virus (ZIKV) in Colombia and Brazil, where the first cases were reported in 2015. The model considers the sexual transmission dynamics of both viruses and vector-host interactions. We begin by exploring the qualitative behaviour of each model separately. We then analyze the dynamics of the co-infection model using the thresholds and results defined separately for each model. The model also considers the impact of intervention strategies, such as personal protection, antiretroviral therapy (ART), and sexual protection (condom use). Using available and assumed parameter values for Colombia and Brazil, the model is calibrated to investigate the long-term co-infection dynamics, the influence of specific parameters, and the potential effect of implementing these intervention strategies on co-infection spread. The study’s results revealed that the duration of Zika infection is a critical factor influencing the burden of co-infection cases. Additionally, bed nets and use of condoms are essential for disease control, while ART is less emphasized due to the cost-effectiveness of condom use.

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and a latent variable models the dependence between observations in each cluster. We demonstrate the estimation of copula and margin parameters, outlining the procedure for determining the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of its application is given using COVID-19 vaccination hesitancy data from several countries. All developed methodologies are implemented in CopulaGAMM, available in CRAN.

Introduction: Arboviruses are a broad classification of viral pathogens that require vectors such as mosquitoes for infection transmission. The burden of arboviral diseases worldwide is substantial, affecting millions of people annually, with the Aedes aegypti mosquito responsible for spreading several common arboviruses, including dengue, chikungunya, Zika and yellow fever. One public health strategy to control and prevent these viruses is to influence community members’ behaviours related to reducing the breeding sites of Aedes mosquitoes, and knowledge, attitudes and practice (KAP) questionnaires are often used as part of these education campaigns. Objectives: To explore the content of KAP questionnaires and methodologies used to evaluate arboviral infections, focusing on dengue, Zika, chikungunya and yellow fever. Methods and analysis: To identify and describe KAP questionnaires for the selected arboviral infections, a scoping review will be performed and reported according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Scoping Review Extension guidelines. Scientific databases such as MEDLINE, Cochrane, EMBASE, Web of Science, Scielo and LILACS will be searched systematically. Two independent reviewers will screen the title and abstract, followed by a full-text review of the selected articles using the COVIDENCE platform. The extracted information will include citation details, the type of arbovirus, the type of questions in each domain, the scoring system, the theoretical framework and the statistical analysis. The results will be presented comprehensively in tables and figures. Ethics and dissemination: Ethics approval is not required. Knowledge transfer will be conducted through conference presentations and publications.