arXiv subjects

Sara Hamis

Publications and source records attributed to Sara Hamis.

13 recordsLinked to original sources

arXiv2026

Limited knowledge exchange across biological subfields in agent-based modelling: an LLM-assisted bibliometric analysis

Agent-based models (ABMs) are widely used across the biological sciences. While applications differ between biological subfields, the mathematical and statistical methods underlying ABMs largely do not, raising the question of how much knowledge is exchanged between subfields. We address this question by developing a bibliometric pipeline that combines a database keyword search with coarse- and fine-grained classification by a large language model (LLM). We apply the pipeline to the Web of Science Core Collection, classifying 22,936 ABM articles into ecology, epidemiology, oncology, other-biology, or not-biology. Using citation patterns and author overlap as proxies for knowledge exchange, we find that 83%, 81%, and 69% of citations from ecology, epidemiology, and oncology articles, respectively, go to articles in the same subfield. Furthermore, 91% of authors with at least two articles across these subfields publish exclusively within one subfield. Both proportions far exceed those expected under random assignment of subfields (permutation tests, $p \leq 0.001$). Terminology also differs, with "individual-based model" used mainly in ecology and "agent-based model" in epidemiology, oncology, and outside biology. Taken together, our results suggest limited knowledge exchange between biological subfields in ABM research, leading us to discuss opportunities for increased exchange through conferences, journals, and training.

physics.soc-ph↗

arXiv2026

An efficient and flexible generalization of transit compartment models for delayed biological processes

Transit compartment models are widely used in pharmacokinetics/pharmacodynamics to represent delayed biological processes such as absorption, maturation, cellular proliferation, and treatment-induced toxicity. This transit compartment formulation imposes an artificial relationship between the mean and variance of the delay distribution, as the number of transit compartment must be integer-valued number of transit compartments. Consequently, estimating the number of compartments from experimental data leads to mixed-integer optimization problems that artificially constrain model dynamics and bias parameter inference. However, these transit compartment models are mathematically equivalent to distributed delay differential equations with Erlang delay kernels. We leverage a hypoexponential generalization of these distributed delay differential equations that preserves the familiar ordinary differential equation structure while allowing the mean and variance of the delay distribution to be estimated directly as real-valued parameters. This approach does not increase the number of inferred parameters and can be immediately implemented as a straightforward modification of existing transit compartment models. We demonstrate the approach using models of viral eclipse phases, lymphocyte proliferation, and chemotherapy-induced neutropenia. Across these examples, the hypoexponential formulation provides comparable or improved fits relative to Erlang transit models and substantially reduces computational cost by avoiding grid search over compartment numbers. This framework provides a practical approach to estimate biologically meaningful delay distributions in quantitative systems pharmacology (QSP) models.

q-bio.QM↗

arXiv2026

Frequentist and Bayesian population pharmacometrics: similarities, differences, and practical implications

Although the frequentist versus Bayesian debate has a long-standing history, and both are well-established approaches for inference, they are often considered separately in pharmacometric literature, with their theoretical and practical differences receiving limited direct comparison. We address this gap by providing a conceptual background and comparative evaluation of frequentist and Bayesian methods for parameter inference in pharmacometrics. First, we highlight the theoretical and algorithmic differences between approaches within a general and pharmacometric context. We then apply both to classical compartmental pharmacokinetic models using simulated and real data; initially through evaluating four inference methods (two frequentist, two Bayesian) across a range of simulated data conditions, followed by investigating each inference approach in the practical setting. The simulation studies facilitate evaluation of the sensitivity of the methods to sample size, number of observations, residual noise and inter-individual variability, comparing the performance with respect to relative error, confidence/credible interval coverage and bias in the estimated variability. The real-world data analysis further highlights how each approach quantifies and presents uncertainty estimates by examining this for both the parameter estimates and system dynamics. By providing a theoretical and practical comparison that highlights the similarities and differences between approaches, this work aims to lower the barrier to understanding and implementing Bayesian and frequentist inference in pharmacometrics.

stat.ME↗

arXiv2026

Hyperparameter selection for equation learning with biologically-informed neural networks

Biologically-informed neural networks (BINNs) have emerged as a flexible subclass of physics-informed neural networks (PINNs) for learning terms in partial differential equations from data. BINNs are particularly suited for biological systems, where the governing equations are highly nonlinear and only partially known a priori, and where data observations are often sparse, noisy, and incomplete. However, applying BINNs effectively in practice depends critically on hyperparameter selection, which remains a central challenge in equation-learning frameworks. Hyperparameters are often chosen heuristically and only cursorily documented, which limits the reproducibility of results and the transferability of methods. We present a diagnostic workflow for hyperparameter selection that can be used when the ground-truth equations are not known. The workflow is guided by three main questions: (1) Are the benefits of greater network capacity worth the cost? (2) Do more training epochs keep reducing the validation loss? (3) Do the learned terms stop changing as network capacity and training increase? We apply our workflow to synthetic systems of varying complexity with known ground truth, spanning diffusion and growth right-hand side terms and data ranging from 1D+t to 2D+t. We demonstrate that the validation loss generally follows the true error in the learned terms and distil practical rules of thumb for selecting hyperparameters in the BINN architecture. By providing a structured workflow, practical guidelines, and suggested starting values for hyperparameter selection, this work lowers the barrier to BINN-based equation learning.

cs.LG↗

arXiv2026

The MCMC convergence graph: a diagnostic for multimodal posteriors

Multimodality is common in many scientific and engineering applications. However, standard Markov chain Monte Carlo (MCMC) convergence diagnostics often penalise multimodality in practice by conflating overall poor mixing with groups of chains that have mixed well within distinct modes. To diagnose multimodality rather than flag it as a sampling failure, we introduce the MCMC convergence graph: a graph-based diagnostic that computes pairwise R-hat values between chains and summarises them in a graph, revealing sets of chains that explore the same posterior mode. We implement the method in the probabilistic programming framework Stan and demonstrate its use on worked examples ranging from regression models with inherent multimodality in the data, to a pharmacokinetic model for which multimodality reflects non-identifiability. The graph-based diagnostic, which we make freely available in the R package mcmcConvergenceGraph and which accepts MCMC output from any sampler, provides both graphical and numerical summaries of MCMC behaviour for diagnosing multimodality.

stat.ME↗

arXiv2026

Adaptive therapy under parametric, structural, and measurement uncertainty

Adaptive therapy has emerged as a promising treatment strategy that exploits within-tumour competition to delay disease progression. Implementation, however, typically relies on indirect measurements of tumour burden and must account for potentially substantial patient heterogeneity. In this work, we capture patient-to-patient variability, parameter uncertainty, and imperfect biomarker measurements with a mathematical and statistical model that we calibrate to clinical prostate cancer data using a Bayesian inference framework. We use the resulting virtual cohort to demonstrate that, within the simple but now well-established Lotka-Volterra-based model, adaptive therapy robustly improves time-to-progression for the subset of patients that are predicted to eventually progress by the model. To account for other risk factors associated with larger tumour volumes, we introduce a new metric based on the risk of metastasis that demonstrates how adaptive therapy may be disadvantageous when sustained tumour burden is also considered. Given the ubiquity of uncertainty in oncology, we then describe several future modelling directions that also capture uncertainty in the temporal evolution of the underlying tumour or biomarker dynamics. Finally, we demonstrate how model misspecification and non-identifiability can lead to unreliable predictions, especially if uncertainty is inadequately captured.

q-bio.TO↗

arXiv2026

A practical introduction to ODE modelling in Stan for biological systems

Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these purposes. One such tool is Stan, a freely available and open-source probabilistic programming framework that provides efficient methods for estimating model parameters from data using computational Bayesian inference algorithms. Stan includes built-in mechanisms for working with ordinary differential equation (ODE) models, which are widely used in mathematical biology and related fields to study simulated, experimental, and real-world systems that change over time. Through step-by-step worked examples, including both pedagogical toy models and applications with real data, this article provides a practical, self-contained introduction to performing parameter estimation and model evaluation for first-order linear and nonlinear ODE models in Stan. The article also explains key statistical methods that underpin Stan and discusses computational Bayesian modelling in the context of biological applications.

stat.CO↗

arXiv2026

Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential operator structure (e.g., reaction-diffusion) while learning constitutive terms via trainable neural subnetworks, enforced through soft residual penalties. Existing BINN studies are limited to $1\mathrm{D}{+}t$ reaction-diffusion systems and focus on forward prediction, using the governing partial differential equation as a regulariser rather than an explicit identification target. Here, we extend BINNs to $2\mathrm{D}{+}t$ systems within a PINN framework that combines data preprocessing, BINN-based equation learning, and symbolic regression post-processing for closed-form equation discovery. We demonstrate the framework's real-world applicability by learning the governing equations of lung cancer cell population dynamics from time-lapse microscopy data, recovering $2\mathrm{D}{+}t$ reaction-diffusion models from experimental observations. The proposed framework is readily applicable to other spatio-temporal systems, providing a practical and interpretable tool for fast analytic equation discovery from data.

cs.LG↗

arXiv2025

A nonparametric approach to practical identifiability of nonlinear mixed effects models

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread adoption of this individual-based fitting, it is becoming increasingly common to take a hierarchical approach to parameter estimation, where modellers characterize the population parameter distributions, rather than considering each individual independently. This hierarchical parameter estimation is standard in pharmacometric modelling. However, many of the existing techniques for parameter identifiability do not immediately translate from the individual-based fitting to the hierarchical setting. Here, we propose a nonparametric approach to study practical identifiability within a hierarchical parameter estimation framework. We focus on the commonly used nonlinear mixed effects framework and investigate two well-studied examples from the pharmacometrics and viral dynamics literature to illustrate the potential utility of our approach.

stat.ME↗

arXiv2025

A bibliometric study on mathematical oncology: interdisciplinarity, internationality, collaboration and trending topics

Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers are incentivised to quickly adapt to both technical and medical research advances. Determining the scope of mathematical oncology is therefore not straightforward; however, it is important for purposes related to funding allocation, education, scientific communication, and community organisation. To address this issue, we here conduct a bibliometric analysis of mathematical oncology. We compare our results to the broader field of mathematical biology, and position our findings within theoretical science of science frameworks. Based on article metadata and citation flows, our results provide evidence that mathematical oncology has undergone a significant evolution since the 1960s marked by increased interactions with other disciplines, geographical expansion, larger research teams, and greater diversity in studied topics. The latter finding contributes to the greater discussion on which models different research communities consider to be valuable in the era of big data and machine learning. Further, the results presented in this study quantitatively motivate that international collaboration networks should be supported to enable new countries to enter and remain in the field, and that mathematical oncology benefits both mathematics and the life sciences.

physics.soc-ph↗

arXiv2025

Phenotypic heterogeneity in temporally fluctuating environments

Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a discrete (often binary) set of phenotypes specialised to each condition. In this work, we extend theory on both fronts to encapsulate a potentially continuous spectrum of phenotypes arising in response to environmental fluctuations that drive changes in the phenotype-dependent growth rate. We consider two broad classes of stochastic environment: those that are temporally uncorrelated (modelled by white-noise processes), and those that are correlated (modelled by Poisson and Ornstein-Uhlenbeck processes). For tractability, we restrict analysis to an exponential growth model, and consider biologically relevant simplifications that pertain to the timescale of phenotype switching relative to fluctuations in the environment. These assumptions yield a series of analytical and semi-analytical expressions that reveal environments in which phenotypic heterogeneity is evolutionarily advantageous.

q-bio.PE↗

arXiv2025

Reducing phenotype-structured PDE models of cancer evolution to systems of ODEs: a generalised moment dynamics approach

Intratumour phenotypic heterogeneity is nowadays understood to play a critical role in disease progression and treatment failure. Accordingly, there has been increasing interest in the development of mathematical models capable of capturing its role in cancer cell adaptation. This can be systematically achieved by means of models comprising phenotype-structured nonlocal partial differential equations, tracking the evolution of the phenotypic density distribution of the cell population, which may be compared to gene and protein expression distributions obtained experimentally. Nevertheless, given the high analytical and computational cost of solving these models, much is to be gained from reducing them to systems of ordinary differential equations for the moments of the distribution. We propose a generalised method of model-reduction, relying on the use of a moment generating function, Taylor series expansion and truncation closure, to reduce a nonlocal reaction-advection-diffusion equation, with general phenotypic drift and proliferation rate functions, to a system of moment equations up to arbitrary order. Our method extends previous results in the literature, which we address via two examples, by removing any \textit{a priori} assumption on the shape of the distribution, and provides a flexible framework for mathematical modellers to account for the role of phenotypic heterogeneity in cancer adaptive dynamics, in a simpler mathematical framework.

q-bio.PE↗

arXiv2020

Uncertainty and Sensitivity Analyses Methods for Agent-Based Mathematical Models: An Introductory Review

Multiscale, agent-based mathematical models of biological systems are often associated with model uncertainty and sensitivity to parameter perturbations. Here, three uncertainty and sensitivity analyses methods, that are suitable to use when working with agent-based models, are discussed. These methods are namely Consistency Analysis, Robustness Analysis and Latin Hypercube Analysis. This introductory review discusses origins, conventions, implementation and result interpretation of the aforementioned methods. Information on how to implement the discussed methods in MATLAB is included.

stat.ME↗