We introduce and discuss a kinetic framework describing the time evolution of the statistical distributions of a population divided into the compartments of susceptible, infectious, recovered, and resistant in the presence of a microbial infection driven by susceptible infectious interactions. Our main objective is to quantify the impact of excessive and inappropriate antimicrobial use, which accelerates the spread of resistance by enabling a fraction of infectious individuals to transition into the resistant compartment. The model consists of a system of Boltzmann type equations capturing binary interactions between susceptible and infectious individuals, complemented by linear redistribution operators that represent recovery, the development of resistance, and reinfection processes. In the grazing collision limit, we show that this Boltzmann system is well approximated by a system of coupled Fokker Planck equations. This limiting description allows for a more tractable analysis of the dynamics, including the characterization of the long-time behavior of the population densities. Our analysis highlights how interaction terms drive the system toward a stable equilibrium and quantif
The evolution of antimicrobial resistance generally occurs in an environment where antimicrobial concentration is variable, which has dramatic consequences on the microorganisms' fitness landscape, and thus on the evolution of resistance. We investigate the effect of these time-varying patterns of selection within a stochastic model. We consider a homogeneous microbial population of fixed size subjected to periodic alternations of phases of absence and presence of an antimicrobial that stops growth. Combining analytical approaches and stochastic simulations, we quantify how the time necessary for fit resistant bacteria to take over the microbial population depends on the alternation period. We demonstrate that fast alternations strongly accelerate the evolution of resistance, reaching a plateau for sufficiently small periods. Furthermore, this acceleration is stronger in larger populations. For asymmetric alternations, featuring a different duration of the phases with and without antimicrobial, we shed light on the existence of a minimum for the time taken by the population to fully evolve resistance. The corresponding dramatic acceleration of the evolution of antimicrobial resista
The evolution of antimicrobial resistance can be strongly affected by variations of antimicrobial concentration. Here, we study the impact of periodic alternations of absence and presence of antimicrobial on resistance evolution in a microbial population, using a stochastic model that includes variations of both population composition and size, and fully incorporates stochastic population extinctions. We show that fast alternations of presence and absence of antimicrobial are inefficient to eradicate the microbial population and strongly favor the establishment of resistance, unless the antimicrobial increases enough the death rate. We further demonstrate that if the period of alternations is longer than a threshold value, the microbial population goes extinct upon the first addition of antimicrobial, if it is not rescued by resistance. We express the probability that the population is eradicated upon the first addition of antimicrobial, assuming rare mutations. Rescue by resistance can happen either if resistant mutants preexist, or if they appear after antimicrobial is added to the environment. Importantly, the latter case is fully prevented by perfect biostatic antimicrobials th
We compare the network of aggregated journal-journal citation relations provided by the Journal Citation Reports (JCR) 2012 of the Science and Social Science Citation Indexes (SCI and SSCI) with similar data based on Scopus 2012. First, global maps were developed for the two sets separately; sets of documents can then be compared using overlays to both maps. Using fuzzy-string matching and ISSN numbers, we were able to match 10,524 journal names between the two sets; that is, 96.4% of the 10,936 journals contained in JCR or 51.2% of the 20,554 journals covered by Scopus. Network analysis was then pursued on the set of journals shared between the two databases and the two sets of unique journals. Citations among the shared journals are more comprehensively covered in JCR than Scopus, so the network in JCR is denser and more connected than in Scopus. The ranking of shared journals in terms of indegree (that is, numbers of citing journals) or total citations is similar in both databases overall (Spearman's \r{ho} > 0.97), but some individual journals rank very differently. Journals that are unique to Scopus seem to be less important--they are citing shared journals rather than bein
Antimicrobial Resistance (RAM) poses a significant threat to global public health, making important medicines less useful. While the medical and biological reasons behind RAM are well studied, we still don't know enough about how false health information affects people's actions, which can speed up RAM. This study presents a new mathematical model to investigate the complex interplay between the spread of misinformation and the dynamics of RAM. We adapt a multi-strain fake news model, including distinct population compartments representing individuals susceptible to, believing in, or skeptical of various ideas related to antibiotic use. The model considers multiple "strains" of misinformation, such as the wrong belief that antibiotics are effective for viral infections or not trusting medical advice regarding prudent antibiotic prescription. Time delays are integrated to reflect the latency in information processing, behavioral change, and the manifestation of resistance. Through stability analysis and numerical simulations, this research aims to identify critical factors and parameters that influence the propagation of harmful beliefs and their consequent impact on behaviors contr
Accurate and timely identification of hospital outbreak clusters is crucial for preventing the spread of infections that have epidemic potential. While assessing pathogen similarity through whole genome sequencing (WGS) is considered the gold standard for outbreak detection, its high cost and lengthy turnaround time preclude routine implementation in clinical laboratories. We explore the utility of two rapid and cost-effective alternatives to WGS, matrix-assisted laser desorption ionization-time of flight (MALDI-TOF) mass spectrometry and antimicrobial resistance (AR) patterns. We develop a machine learning framework that extracts informative representations from MALDI-TOF spectra and AR patterns for outbreak detection and explore their fusion. Through multi-species analyses, we demonstrate that in some cases MALDI-TOF and AR have the potential to reduce reliance on WGS, enabling more accessible and rapid outbreak surveillance.
Rankings of scholarly journals based on citation data are often met with skepticism by the scientific community. Part of the skepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of authors. This paper focuses on analysis of the table of cross-citations among a selection of Statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care in order to avoid potential over-interpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's Research Assessment Exercise shows strong correlation at aggregate level between assessed research quality and journal citation `export scores' within the discipline of Statistics.
Antimicrobial protocols - using substances such as antibiotics or disinfectants - remain the preferred option for preventing the spread of pathogenic bacteria. However, bacteria can develop mechanisms to reduce their antimicrobial susceptibility, which can lead to treatment failure and the selection of resistance or tolerance. In this work, we propose a minimal population dynamics model to study bacterial selection during cyclic antimicrobial application, a commonly used protocol. Selection in bacterial populations with heterogeneous antimicrobial susceptibility is modelled here as a trade-off between survival advantage (reduction in antimicrobial killing) and potential fitness costs (reduction in growth rate) of the less susceptible strains. The proposed model allows us to derive useful expressions for determining the success of cyclic antimicrobial treatments based on two bacterial traits: growth and kill rates. The results obtained here are directly applicable to preventing the selection and spread of resistant and tolerant bacterial strains in real-life protocols.
Background: Antimicrobial resistance (AMR) is a major global public health problem, contributing to an estimated 4.95 million deaths in 2019 and projected to cause up to 10 million deaths annually and 100 trillion dollars in cumulative economic losses by 2050. Its emergence and spread result from complex biological, ecological, and socioeconomic interactions. Mathematical modelling is a key tool to study AMR dynamics, yet the literature remains fragmented and methodologically limited. This review synthesizes recent mathematical modelling studies to identify trends, biases, and research gaps. Methods: A scoping review following PRISMA-ScR guidelines was conducted. PubMed, Web of Science, and Scopus were searched for studies published between 2019 and 2024 that developed mathematical models of AMR. After screening and duplicate removal, 36 studies were included. Data were extracted using a structured framework covering model context, construction and parameters, and outputs and validation. Results: Most studies relied on deterministic ordinary differential equation (ODE) models and focused on bacterial resistance in human hosts, with only one adopting a One Health perspective. Conjug
There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behavior leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is however greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modeled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterised by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditi
Antimicrobial resistance (AMR) poses a mounting global health crisis, requiring rapid and reliable prediction frameworks that capture its complex evolutionary dynamics. Traditional antimicrobial susceptibility testing (AST), while accurate, remains laborious and time-consuming, limiting its clinical scalability. Existing computational approaches, primarily reliant on single nucleotide polymorphism (SNP)-based analysis, fail to account for evolutionary drivers such as horizontal gene transfer (HGT) and genome-level interactions. This study introduces a novel Evolutionary Mixture of Experts (Evo-MoE) framework that integrates genomic sequence analysis, machine learning, and evolutionary algorithms to model and predict AMR evolution. A Mixture of Experts model, trained on labeled genomic data for multiple antibiotics, serves as the predictive core, estimating the likelihood of resistance for each genome. This model is embedded as a fitness function within a Genetic Algorithm designed to simulate AMR development across generations. Each genome, encoded as an individual in the population, undergoes mutation, crossover, and selection guided by predicted resistance probabilities. The resu
Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from cooperative behaviour. Moreover, microbes generally evolve in volatile environments that, together with demographic fluctuations (birth and death events), drastically alter population size and strain survival. Motivated by the need to better understand the evolution of AMR, we study a population of time-varying size consisting of two competing strains, one drug-resistant and one drug-sensitive, subject to demographic and environmental variability. This is modelled by a binary carrying capacity randomly switching between mild and harsh environmental conditions, and driving the fluctuating volume (total amount of nutrients and antimicrobials at fixed concentration), and thus the size of the community (number of resistant and sensitive cells). We assume that AMR is a shared public good when the concentration of resistant cells exceeds a fixed concentration cooperation threshold, above which the sensitive strain has a growth advantage, whereas resistant cells dominate below it. Using computational means, and devising an analytical treatment (built on suitable quenche
The acquisition of Antimicrobial Multidrug Resistance (AMR) in patients admitted to the Intensive Care Units (ICU) is a major global concern. This study analyses data in the form of multivariate time series (MTS) from 3476 patients recorded at the ICU of University Hospital of Fuenlabrada (Madrid) from 2004 to 2020. 18\% of the patients acquired AMR during their stay in the ICU. The goal of this paper is an early prediction of the development of AMR. Towards that end, we leverage the time-series cluster kernel (TCK) to learn similarities between MTS. To evaluate the effectiveness of TCK as a kernel, we applied several dimensionality reduction techniques for visualization and classification tasks. The experimental results show that TCK allows identifying a group of patients that acquire the AMR during the first 48 hours of their ICU stay, and it also provides good classification capabilities.
Background: Antimicrobial resistance (AMR) is a global health threat. While the WHO Global Antimicrobial Resistance and Use Surveillance System (GLASS) provides standardized data, population-level machine learning forecasting of resistance trends remains limited. Translating computational forecasts into policy requires transparent interpretation mechanisms. Methods: Surveillance data (2021-2023) comprising 5,909 observations across 44 countries and five WHO regions were processed. A rigorous temporal split prevented data leakage. Six models (Naive, Linear, Ridge, XGBoost, LightGBM, LSTM) were benchmarked to forecast one-year-ahead resistance rates using features including prior-year resistance and antibiotic consumption. Evaluation metrics (MAE, RMSE, sMAPE) were computed, with 95% bootstrap confidence intervals for MAE. A local Retrieval-Augmented Generation (RAG) system utilizing Gemma 4 was implemented to translate forecast findings into policy guidance grounded in retrieved WHO documents. Results: XGBoost achieved the best performance (test MAE = 6.13% [95% CI: 5.83-6.44]), an 85.3% error reduction versus the naive baseline (MAE = 41.79%). SHAP analysis identified prior-year re
In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangians for cone constrained programs within a unified framework. We develop a new general method for proving the existence of global saddle points of augmented Lagrangian functions, called the localization principle. The localization principle unifies, generalizes and sharpens most of the known results on existence of global saddle points, and, in essence, reduces the problem of the existence of saddle points to a local analysis of optimality conditions. With the use of the localization principle we obtain first necessary and sufficient conditions for the existence of a global saddle point of an augmented Lagrangian for cone constrained minimax problems via both second and first order optimality conditions. In the second part of the paper, we present a general approach to the construction of globally exact augmented Lagrangian functions. The general approach developed in this paper allowed us not only to sharpen most of the existing results on globally exact augmented Lagrangians, but also to construct first
We propose a mathematical model of Antimicrobial Resistance in the host to predict the failure of two antagonists of bacterial growth: the immune response and a single-antibiotic therapy. After characterising the initial bacterial load that cannot be cleared by the immune system alone, we define the success set of initial conditions for which an infection-free equilibrium can be reached by a viable single-antibiotic therapy, and we provide a rigorously defined inner approximation of the set. For initial conditions within the success set, we propose an optimal control framework to design single-drug therapies.
Using the Scopus dataset (1996-2007) a grand matrix of aggregated journal-journal citations was constructed. This matrix can be compared in terms of the network structures with the matrix contained in the Journal Citation Reports (JCR) of the Institute of Scientific Information (ISI). Since the Scopus database contains a larger number of journals and covers also the humanities, one would expect richer maps. However, the matrix is in this case sparser than in the case of the ISI data. This is due to (i) the larger number of journals covered by Scopus and (ii) the historical record of citations older than ten years contained in the ISI database. When the data is highly structured, as in the case of large journals, the maps are comparable, although one may have to vary a threshold (because of the differences in densities). In the case of interdisciplinary journals and journals in the social sciences and humanities, the new database does not add a lot to what is possible with the ISI databases.
Antimicrobial Resistance (AMR) is a rapidly escalating global health crisis. While genomic sequencing enables rapid prediction of resistance phenotypes, current computational methods have limitations. Standard machine learning models treat the genome as an unordered collection of features, ignoring the sequential context of Single Nucleotide Polymorphisms (SNPs). State-of-the-art sequence models like Transformers are often too data-hungry and computationally expensive for the moderately-sized datasets that are typical in this domain. To address these challenges, we propose AMR-EnsembleNet, an ensemble framework that synergistically combines sequence-based and feature-based learning. We developed a lightweight, custom 1D Convolutional Neural Network (CNN) to efficiently learn predictive sequence motifs from high-dimensional SNP data. This sequence-aware model was ensembled with an XGBoost model, a powerful gradient boosting system adept at capturing complex, non-local feature interactions. We trained and evaluated our framework on a benchmark dataset of 809 E. coli strains, predicting resistance across four antibiotics with varying class imbalance. Our 1D CNN-XGBoost ensemble consis
Antimicrobial resistance is an important public health concern that has implications in the practice of medicine worldwide. Accurately predicting resistance phenotypes from genome sequences shows great promise in promoting better use of antimicrobial agents, by determining which antibiotics are likely to be effective in specific clinical cases. In healthcare, this would allow for the design of treatment plans tailored for specific individuals, likely resulting in better clinical outcomes for patients with bacterial infections. In this work, we present the recent work of Drouin et al. (2016) on using Set Covering Machines to learn highly interpretable models of antibiotic resistance and complement it by providing a large scale application of their method to the entire PATRIC database. We report prediction results for 36 new datasets and present the Kover AMR platform, a new web-based tool allowing the visualization and interpretation of the generated models.
Antimicrobial resistance (AMR) is a global threat and combating its spread is of paramount importance. AMR often results from a cooperative behaviour with shared drug protection. Microbial communities generally evolve in volatile, spatially structured settings. Migration, space, fluctuations, and environmental variability all have a significant impact on the development and proliferation of AMR. While drug resistance is enhanced by migration in static conditions, this changes in time-fluctuating spatially structured environments. Here, we consider a two-dimensional metapopulation consisting of demes in which drug-resistant and sensitive cells evolve in a time-changing environment. This contains a toxin against which protection can be shared (cooperative AMR). Cells migrate between demes and connect them. When the environment and the deme composition vary on the same timescale, strong population bottlenecks cause fluctuation-driven extinction events, countered by migration. We investigate the influence of migration and environmental variability on the AMR eco-evolutionary dynamics by asking at what migration rate fluctuations can help clear resistance and what are the near-optimal e