Temporal trends in calls for suicide attempts to poison control centers in France during the COVID-19 pandemic: a nationwide study.

Concerns have been raised about early vs. later impacts of the COVID-19 pandemic on suicidal behavior. However, data remain sparse to date. We investigated all calls for intentional drug or other toxic ingestions to the eight Poison Control Centers in France between 1st January 2018 and 31st May 2022. Data were extracted from the French National Database of Poisonings. Calls during the study period were analyzed using time trends and time series analyses with SARIMA models (based on the first two years). Breakpoints were determined using Chow test. These analyses were performed together with examination of age groups (≤ 11, 12-24, 25-64, ≥ 65 years) and gender effects when possible. Over the studied period, 66,589 calls for suicide attempts were received. Overall, there was a downward trend from 2018, which slowed down in October 2019 and was followed by an increase from November 2020. Number of calls observed during the COVID period were above what was expected. However, important differences were found according to age and gender. The increase in calls from mid-2020 was particularly observed in young females, while middle-aged adults showed a persisting decrease. An increase in older-aged people was observed from mid-2019 and persisted during the pandemic. The pandemic may therefore have exacerbated a pre-existing fragile situation in adolescents and old-aged people. This study emphasizes the rapidly evolving situation regarding suicidal behaviour during the pandemic, the possibility of age and gender differences in impact, and the value of having access to real-time information to monitor suicidal acts.

Inference with selection, varying population size, and evolving population structure: application of ABC to a forward-backward coalescent process with interactions.

Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed a priori known, the evolution of the genetic composition of a population does not affect demography nor population structure, and there is no selection nor interaction between and within genetic strains. In this paper, we present a stochastic birth-death model with competitive interactions and asexual reproduction. We develop an inferential procedure for ecological, demographic, and genetic parameters. We first show how genetic diversity and genealogies are related to birth and death rates, and to how individuals compete within and between strains. This leads us to propose an original model of phylogenies, with trait structure and interactions, that allows multiple merging. Second, we develop an Approximate Bayesian Computation framework to use our model for analyzing genetic data. We apply our procedure to simulated data from a toy model, and to real data by analyzing the genetic diversity of microsatellites on Y-chromosomes sampled from Central Asia human populations in order to test whether different social organizations show significantly different fertilities.

Hepatitis C treatment as prevention of viral transmission and liver-related morbidity in persons who inject drugs.

UNLABELLED: Hepatitis C virus (HCV) seroprevalence remains high in people who inject drug (PWID) populations, often above 60%. Highly effective direct-acting antiviral (DAA) regimens (90% efficacy) are becoming available for HCV treatment. This therapeutic revolution raises the possibility of eliminating HCV from this population. However, for this, an effective cascade of care is required. In the context of the available DAA therapies, we used a dynamic individual-based model including a model of the PWID social network to simulate the impact of improved testing, linkage to care, and adherence to treatment, and of modified treatment recommendation on the transmission and on the morbidity of HCV in PWID in France. Under the current incidence and cascade of care, with treatment initiated at fibrosis stage ≥F2, HCV prevalence decreased from 42.8% to 24.9% (95% confidence interval: 24.8-24.9) after 10 years. Changing treatment initiation criteria to treat from F0 was the only intervention leading to a substantial additional decrease in prevalence, which fell to 11.6% (95% CI: 11.6-11.7) at 10 years. Combining this change with improved testing, linkage to care, and adherence to treatment decreased HCV prevalence to 7.0% (95% CI: 7.0-7.1) at 10 years and avoided 15% (95% CI: 14-17) and 29% (95% CI: 28-30) of cirrhosis complications over 10 and 40 years, respectively. CONCLUSIONS: Major decreases in prevalent HCV infections occur only when treatment is initiated at early stages of fibrosis, suggesting that systematic treatment in PWID, where incidence remains high, would be beneficial. However, elimination within the 10 next years will be difficult to achieve using treatment alone, even with a highly improved cascade of care.

The need for treatment scale-up to impact HCV transmission in people who inject drugs in Montréal, Canada: a modelling study.

BACKGROUND: HCV transmission remains high in people who inject drugs (PWID) in Montréal. New direct-acting antivirals (DAAs), highly effective and more tolerable than previous regimens, make a "Treatment as Prevention" (TasP) strategy more feasible. This study assesses how improvements in the cascade of care could impact hepatitis C burden among PWID in Montréal. METHODS: We used a dynamic model to simulate HCV incidence and prevalence after 10 years, and cirrhosis complications after 10 and 40 years. Eight scenarios of improved cascade of care were examined. RESULTS: Using a baseline incidence and prevalence of 22.1/100 person-years (PY) and 53.1%, implementing the current cascade of care using DAAs would lead to HCV incidence and prevalence estimates at 10 years of 9.4/100PY and 55.8%, respectively. Increasing the treatment initiation rate from 5%/year initially to 20%/year resulted in large decreases in incidence (6.4/100PY), prevalence (36.6%), and cirrhosis complications (-18%/-37% after 10/40 years). When restricting treatment to fibrosis level ≥ F2 instead of F0 (reference scenario), such decreases in HCV occurrence were unreachable. Improving the whole cascade of care led to the greatest effect by halving both the incidence and prevalence at 10 years, and the number of cirrhosis complications after 40 years. CONCLUSIONS: The current level of treatment access in Montréal is limiting a massive decrease in hepatitis C burden among PWID. A substantial treatment scale-up, regardless of fibrosis level, is necessary. While improving the rest of the cascade of care is necessary to optimize a TasP strategy and control the HCV epidemic, a treatment scale-up is first needed.

The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism.

Horizontal transfer (HT) of heritable information or 'traits' (carried by genetic elements, plasmids, endosymbionts, or culture) is widespread among living organisms. Yet current ecological and evolutionary theory addressing HT is scant. We present a modeling framework for the dynamics of two populations that compete for resources and horizontally exchange (transfer) an otherwise vertically inherited trait. Competition influences individual demographics, thereby affecting population size, which feeds back on the dynamics of transfer. This feedback is captured in a stochastic individual-based model, from which we derive a general model for the contact rate, with frequency-dependent (FD) and density-dependent (DD) rates as special cases. Taking a large-population limit on the stochastic individual-level model yields a deterministic Lotka-Volterra competition system with additional terms accounting for HT. The stability analysis of this system shows that HT can revert the direction of selection: HT can drive invasion of a deleterious trait, or prevent invasion of an advantageous trait. Due to HT, invasion does not necessarily imply fixation. Two trait values may coexist in a stable polymorphism even if their invasion fitnesses have opposite signs, or both are negative. Addressing the question of how the stochasticity of individual processes influences population fluctuations, we identify conditions on competition and mode of transfer (FD versus DD) under which the stochasticity of transfer events overwhelms demographic stochasticity. Assuming that one trait is initially rare, we derive invasion and fixation probabilities and time. In the case of costly plasmids, which are transfered unilaterally, invasion is always possible if the transfer rate is large enough; under DD and for intermediate values of the transfer rate, maintenance of the plasmid in a polymorphic population is possible. In conclusion, HT interacts with ecology (competition) in non-trivial ways. Our model provides a basis to model the influence of HT on evolutionary adaptation.

On computer-intensive simulation and estimation methods for rare-event analysis in epidemic models.

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of public health. In general, no close analytic form for their occurrence probabilities is available, and crude Monte Carlo procedures fail. We show how recent intensive computer simulation techniques, such as interacting branching particle methods, can be used for estimation purposes, as well as for generating model paths that correspond to realizations of such events. Applications of these simulation-based methods to several epidemic models fitted from real datasets are also considered and discussed thoroughly.

Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks.

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.

Daphnias: from the individual based model to the large population equation.

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61:277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23:114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4:82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and through their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., loc. cit.).

A general stochastic model for sporophytic self-incompatibility.

Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class cannot mate. We model pollen limitation through different relationships between mate availability and fertilization success. After deriving a general stochastic model, we focus on the simple case of distylous plant species where only two classes of individuals exist. We first study the dynamics of such a species in a large population limit and then, we look for an approximation of the extinction probability in small populations. This leads us to consider inhomogeneous random walks on the positive quadrant. We compare the dynamics of distylous species to self-fertile species with and without inbreeding depression, to obtain the conditions under which self-incompatible species can be less sensitive to extinction while they can suffer more pollen limitation.

New first-trimester crown-rump length equations from a French general population.

INTRODUCTION: The purpose of this study was to obtain precise knowledge of fetal biometric measurements, in particular crown-rump length (CRL). Our results have been carefully compared to equations found in the literature. MATERIALS AND METHODS: Single-operator measurements of 2,123 spontaneous pregnancies from a general French population provided new statistical relationships between fetal age (FA) and CRL. Comparisons were made with measurements obtained from 402 in vitro fertilizations (IVFs) for which FA were known. Heteroskedastic and robust regressions were compared by cross-validation, and prediction errors were studied. All ultrasound measurements were taken during standard follow-ups of pregnancies, without any additional features. RESULTS: From a cleaned subsample of 513 spontaneous pregnancies, we reported good modeling of first-term embryonic growth, with equations and predictions of standard deviations agreeing with objective datations for IVFs. Most precise CRL measurements were predicted for FA of 49 days. DISCUSSION: Our results allow future detection of fetal growth abnormalities using Z-scores throughout the first trimester.

HIV with contact tracing: a case study in approximate Bayesian computation.

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian computation (ABC), an alternative to data imputation methods such as Markov chain Monte Carlo (MCMC) integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%.

Trait Substitution Sequence process and Canonical Equation for age-structured populations.

We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump process that generalizes the Trait Substitution Sequence process describing Adaptive Dynamics for populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve an establishment probability, describing the probability of invasion of the resident population by the mutant one, that cannot always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.

Predicting data saturation in qualitative surveys with mathematical models from ecological research.

OBJECTIVE: Sample size in surveys with open-ended questions relies on the principle of data saturation. Determining the point of data saturation is complex because researchers have information on only what they have found. The decision to stop data collection is solely dictated by the judgment and experience of researchers. In this article, we present how mathematical modeling may be used to describe and extrapolate the accumulation of themes during a study to help researchers determine the point of data saturation. STUDY DESIGN AND SETTING: The model considers a latent distribution of the probability of elicitation of all themes and infers the accumulation of themes as arising from a mixture of zero-truncated binomial distributions. We illustrate how the model could be used with data from a survey with open-ended questions on the burden of treatment involving 1,053 participants from 34 different countries and with various conditions. The performance of the model in predicting the number of themes to be found with the inclusion of new participants was investigated by Monte Carlo simulations. Then, we tested how the slope of the expected theme accumulation curve could be used as a stopping criterion for data collection in surveys with open-ended questions. RESULTS: By doubling the sample size after the inclusion of initial samples of 25 to 200 participants, the model reliably predicted the number of themes to be found. Mean estimation error ranged from 3% to 1% with simulated data and was <2% with data from the study of the burden of treatment. Sequentially calculating the slope of the expected theme accumulation curve for every five new participants included was a feasible approach to balance the benefits of including these new participants in the study. In our simulations, a stopping criterion based on a value of 0.05 for this slope allowed for identifying 97.5% of the themes while limiting the inclusion of participants eliciting nothing new in the study. CONCLUSION: Mathematical models adapted from ecological research can accurately predict the point of data saturation in surveys with open-ended questions.

Inferring R0 in emerging epidemics-the effect of common population structure is small.

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort.

A stochastic SIR model with contact-tracing: large population limits and statistical inference.

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.