Mathematics

Within many bacterial colonies, persister cells exist as a subpopulation that is tolerant to antibiotics and other stressors, yet not genetically distinct from the rest of the colony. A recent study has proposed epigenetic inheritance as a mechanism that leads to the presence of persister cells. We analyze a nonlocal PDE-ODE model introduced in that study to describe the epigenetic inheritance process and establish its mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions. We identify a sharp parameter threshold delineating extinction from persistence of the colony: below this threshold the washout equilibrium is globally asymptotically stable, while above it a unique positive equilibrium exists and the population is weakly persistent. Notably, this threshold is independent of the internal community structure.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

Tetanus is a severe disease of the nervous system, transmitted through bacteria in the environment. In the absence of medical attention, case fatality rates are extremely high. Despite progress towards maternal and neonatal tetanus elimination targets, tetanus remains a serious public health problem. Routine infant and maternal vaccination have contributed to considerable reduction in cases and deaths from tetanus globally. However, protective immunity wanes over time. To increase duration of protection, the World Health Organization recommends three diphtheria-tetanus-pertussis-containing vaccine booster doses be given in early childhood, childhood, and adolescence. Evidence to support country-level decision-making about the introduction of these booster doses is critical. We have developed a novel age-structured, deterministic compartmental model of tetanus transmission and vaccination. The model is driven by environmental transmission and incorporates interventions like hygiene and safe birth practices to reduce the magnitude of environmental transmission. It explicitly models vaccination, separating each dose of the primary series, booster doses, and maternal vaccination to capture dose-specific effectiveness and duration of protection. The model captures heterogeneous immunity profiles by dose and age, and the cumulative nature of vaccine-derived protection. The immune dynamics follow the patterns described in literature and can replicate seroprevalence studies, although the exact characterisation of immunity in the literature still has gaps. This model presents a substantial advancement on previously published models and is well positioned to inform tailored vaccination strategies to reduce neonatal and non-neonatal tetanus.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity. Author SummaryAlthough the mechanisms driving seasonality of respiratory disease dynamics have been well-studied in temperate regions, they are unknown in the tropics. In this study, we used a 10-year influenza-like-illness (ILI) daily-reporting data set collected from outpatient clinics in Ho Chi Minh City (HCMC) in Vietnam to investigate the mechanisms associated with annual and nonannual ([~]215 days) periodic patterns in the data. By comparing seven mechanistic models against the data, we showed that the mechanism that best explains respiratory disease dynamics in HCMC is a stochastic susceptible-infected-recovered-susceptible (SIRS) model weakly driven by external drivers including specific humidity, temperature, and school term. The nonannual cycles duration is consistent with the inferred duration of immunity of the model. By showing the nonannual cycle as strong as in the data is only observed in stochastic model, we showed that the observed respiratory disease dynamics in HCMC is under the influence of stochasticity when external drivers are weak.

Human immunodeficiency virus (HIV) persistence remains a major barrier to cure due to the existence of long-lived latent reservoirs that evade immune clearance and persist despite combination antiretroviral therapy (ART). Although ART effectively suppresses viral replication, treatment interruption often leads to rapid viral rebound originating from these latent reservoirs. In this study, we develop a deterministic mathematical model describing the in vivo dynamics of HIV infection incorporating uninfected CD4+ T cells, infected cells, latent reservoirs, deep latent reservoirs, and infectious and non-infectious virions, while explicitly accounting for the therapeutic effects of reverse transcriptase inhibitors (RTIs), protease inhibitors (PIs), and Tat transcription inhibitors. Analytical results establish positivity and boundedness of solutions and derive the effective reproduction number Re using the next-generation matrix approach. Stability analysis shows that the virus-free equilibrium is locally asymptotically stable when Re < 1, while viral persistence occurs when Re > 1. Numerical simulations were performed to investigate therapy interactions, viral rebound following treatment interruption, and the impact of drug efficacy on viral set-points and latent reservoir dynamics. To further explore therapy interactions, three-dimensional viral set-point surfaces and heat maps were generated to examine how combinations of infection inhibition, viral production inhibition, and transcriptional inhibition influence viral dynamics. The simulations reveal that Tat inhibition suppresses viral transcription, thereby reducing the transition of infected cells into productive infection and limiting viral propagation when combined with conventional ART mechanisms. The therapy parameter planes further demonstrate that strong transcriptional inhibition promotes the transition of infected cells into deep latency, supporting the emerging block-and-lock strategy for functional HIV cure. In addition, a three-dimensional eradication boundary surface and therapy cube were constructed to identify regions of parameter space where Re < 1, corresponding to successful viral control. These visualizations show that viral eradication is unlikely when therapies act independently but becomes achievable when multiple therapeutic mechanisms act simultaneously. Overall, the results highlight the critical role of transcriptional inhibition through Tat-targeting therapies in complementing existing ART regimens. By simultaneously suppressing viral replication and promoting deep latency, Tat-based combination strategies may significantly reduce viral rebound and contribute to long-term functional control of HIV infection.

AO_SCPLOWBSTRACTC_SCPLOWThe classification of pediatric brain tumors is investigated using deep learning on hematoxylin and eosin (H&E) and antigen Ki-67 (Ki-67) whole slide images (WSIs) from the Childrens Brain Tumor Network (CBTN) dataset. A total of 1,662 unregistered WSIs (1,047 H&E and 615 Ki-67 images) were analyzed, including low-grade glioma/astrocytoma (grades 1, 2) (LGG), high-grade glioma/astrocytoma (grades 3, 4) (HGG), medulloblastoma (MB), ependymoma (EP) and ganglioglioma. The The aim of this study was to effectively classify pediatric brain tumors using H&E and Ki-67 WSIs individually, and to investigate whether early, intermediate, and late fusion could improve the predictive performance. From each WSI, 224x 224 pixel patches were extracted, and the instance (patch)-level features were obtained using the histology foundation model CONCHv1_5. The instances were aggregated using clustering-constrained attention multiple instance learning (CLAM) for patient-level classification. Model interpretability and explainability was assessed through attention heatmaps, cell density and Ki-67 labelling index (LI) maps. In the binary grade classification between LGG and HGG, the intermediate concatenation fusion achieved the best performance with a balanced accuracy of 0.88 {+/-} 0.05, (p < 0.005) compared to the single-stain models (H&E: 0.84 {+/-} 0.05, Ki-67: 0.86 {+/-} 0.05). For the 5-class tumor type classification, the one-hidden layer late fusion learning model achieved the highest balanced accuracy of 0.83 {+/-} 0.04 (p < 0.005), outperforming the single-stain models (H&E: 0.77 {+/-} 0.05, Ki-67: 0.74 {+/-} 0.05). Overall, most of the fusion approaches outperformed the single-stain models in both classification tasks (p < 0.005). The Ki-67 attention maps demonstrated moderate to strong Spearman correlation ({rho} = 0.576 - 0.823) with the cell density and Ki-67 LI maps, suggesting that these features are associated with the models predictions, although additional features may contribute. The results show that H&E and Ki-67 images provide complementary information, and most of the multi-stain fusion approaches using deep learning improve pediatric brain tumor diagnosis.

Vaccine-acquired immunity plays an important role in controlling the spread of many infectious diseases; however, vaccine efficacy can diminish over time. This work uses a mathematical model to study the effects of waning vaccination-acquired immunity on infection incidence. With an SEIR-type compartmental model that considers both vaccinated and unvaccinated populations (and their mixing), we present mathematical conditions under which vaccinated individuals drive ongoing growth in infections, i.e., over half of the daily incidence arises from vaccinated individuals. Analysis of a mathematical model of COVID-19 spread in the state of Colorado suggests how and for what duration vaccinated individuals could have sustained such growth. Importantly, our model demonstrates that, despite potential for brief vaccinated-driven periods of growth in infections, which occur among unvaccinated-driven periods of growth in infections, increased vaccination coverage always reduces total cases and total hospitalizations. This work provides insight into how waning immunity in vaccinated populations can contribute to ongoing infection incidence and demonstrates the value of complementary interventions to prevent disease spread in vaccinated populations.

Parkinsons Disease (PD) Motor Scores (MDS-UPDRS Part III) are quite noisy. This paper proposes a new methodology for processing these scores by first denoising the scores to enhance the underlying progression signal, and then conducting a high-dimensional analysis which does not sum the scores into a total movement score. The analysis gives novel insights into PD progression heterogeneity: it reveals that the heterogeneity is continuously variable rather than clustered into "subtypes" and that the variability is along two easily understood axes. This analysis also resolves some of the discrepancies in previously reported progression subtypes. Finally, the analysis reveals that patient-specific progression cannot be predicted from baseline using only MDS-UPDRS Part III scores.

Graph-based methods for data representation and analysis are well suited for encoding both data points and their interrelationships. This approach integrates data and topology, enabling the representation of interrelated information. In this study, we represent patient cohorts as cohort graphs and discuss their application for real-world patient data. We particularly focus on developing methods to cluster patients with similar symptoms and examine how bias parameters (such as sex and age group) influence interlinking within CGs, thereby improving results for accurate patient stratification and personalized decision-making in a clinical context. In particular we illustrate how by considering sex and age groups we can improve the symptom-clustering of a patient population with lung and gastro-intestinal cancer. Finally, we discuss the essential role of high-performance computing (HPC) in upscaling analytical methods for CGs.

We systematically evaluate and compare the performance of classical statistical methods (ARIMA), mechanistic compartmental models (SEIR), modern deep learning architectures (LSTM, DLinear, Autoformer), and an emerging time-series foundation model (TabPFN-TS) to forecasts the incidence of Influenza-Like Illness (ILI) across nine European countries. The models are benchmarked against a naive baseline and a multi-model ensemble (RespiCast) created by an initiative of the ECDC. In line with the operational practice of existing forecasting hubs, our entire evaluation is explicitly optimized for short-term horizons (1 to 4 weeks ahead). Interestingly, we found that the foundation model TabPFN-TS allows for great zero-shot inference capabilities. Without any task-specific retraining, it successfully overcomes extreme data scarcity to consistently outperform all other individual architectures, frequently rivalling or surpassing the RespiCast ensemble. Our results highlight how deep learning architectures are severely constrained by extreme data scarcity, typical in epidemic forecasting, requiring targeted endogenous data augmentation to reduce predictive errors. Within the deep learning class of models, we observe that simpler architectures (such as DLinear and LSTM) frequently exhibit greater robustness and outperform complex, attention-based models (such as Autoformer) when data is constrained. Finally, our results show how a weighted ensemble, constructed by fusing all the models, delivers highly robust forecasts in all regions considered. Overall, our findings showcase the transformative potential of zero-shot foundation models in epidemic forecasting and confirm the importance of multi-model ensembles.

AO_SCPLOWBSTRACTC_SCPLOWImbalances in the human microbiome are associated with numerous diseases, highlighting the need for benchmarks that define healthy microbiome composition and identify abnormal deviations. Although the microbiome is increasingly studied as a potential clinical marker, statistical approaches for constructing reference regions of healthy microbiome composition remain relatively underexplored. This work develops statistical methods to construct reference regions for healthy microbiome data, addressing three main challenges. First, since microbiome data contain relative rather than absolute information, standard statistical methods are not directly appropriate. Therefore, microbiome profiles are treated as compositional data satisfying a sum constraint, and log-ratio transformations are used to analyze them in real space while preserving their relative structure. Second, reference regions are constructed as tolerance regions rather than confidence regions, so that they cover a pre-specified proportion of the healthy population with a given confidence level. The proposed framework incorporates both parametric and nonparametric approaches for constructing these tolerance regions. Parametric methods are considered when the ilr-transformed data approximately follow an elliptical distribution, where they can yield smaller regions while maintaining the desired coverage. Nonparametric approaches provide a flexible alternative by avoiding distributional assumptions. Third, because microbiome data are multidimensional and difficult to interpret, quantitative and graphical tools are introduced to assess atypicality and identify which microbial taxa contribute most to deviations from healthy profiles. Simulation studies are conducted to evaluate the performance of the proposed methods. The methodology is then demonstrated by constructing reference regions for healthy microbiome profiles using real-world data. Finally, the approach is applied to microbiome datasets comparing healthy and patient profiles to assess whether patient samples are identified as atypical and to examine which taxa contribute to these deviations. Overall, the proposed framework provides a clear and statistically robust approach for defining healthy microbiome reference regions and detecting atypical microbiome profiles.

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

Ovarian cancer is one of the gynecological cancer types, which, if metastasized and not detected early, can cause deaths among women. Therefore, there is a need to accurately predict drug responses to ovarian cancer. A gynecological pathologist inspects abnormality in tissues, followed by providing a report about patients; however, such a diagnostic process is (1) hard; (2) requires experience; and (3) time consuming. Moreover, existing tools are far from perfect. Hence, we present a computational pipeline to improve predicting drug response pertaining to ovarian cancer, derived as follows. First, we download digital pathology images pertaining to ovarian bevacizumab response from the cancer imaging archive repository. We employed histogram of oriented gradients to images, constructing feature vectors, provided to Fisher linear discriminant analysis to change the representation through dimensionality reduction. Then, we provide reduced-dimensionality data for regression analysis through support vector regression coupled with various kernels and calculating the area under the ROC curve (AUC). Experimental results against transformer-based models (ViT and Swin) and other deep learning (DL) models (VGG16, ResNet50, InceptionV3, MobileNetV2, and EfficientNetB6) demonstrate that our approach with radial kernel (named SVRD+R) yielded an AUC performance improvements of 17% against the best-performing transformer-based model (ViT) while obtaining an AUC performance improvements of 14.9% when compared against the best DL-based model (MobileNetV2). These results demonstrate the superiority and feasibility of our AI-based pipeline when tackling prediction problems pertaining to gynecologic cancer studies. MSC92B05; 68T09

Short-horizon epidemic forecasting is difficult when surveillance series are highly nonstationary and affected by structural change and evolving reporting conditions. This study evaluates statistical models for global daily COVID-19 incidence using a rolling-origin benchmark designed to approximate real-time forecasting under such conditions. Using global incidence data from 22 January to 27 July 2020, we compare naive, seasonal naive, drift, ARIMA(log1p), ETS(log1p), and Prophet(log1p) forecasts at horizons h [isin] {1, 3, 7, 14} days. Structural phases are identified retrospectively on a variance-stabilized scale and used only to stratify forecast errors. Forecast ranking is strongly horizon-dependent. In the full-sample benchmark, drift performs best at the 1-, 7-, and 14-day horizons, while seasonal naive performs best at 3 days. Among the transformed statistical models, ARIMA(log1p) is competitive at short horizons, whereas ETS(log1p) becomes stronger at 7 and 14 days. Diebold-Mariano tests confirm that several of these differences are statistically meaningful, particularly in favor of drift at short and long horizons and in favor of ETS(log1p) over ARIMA(log1p) at longer horizons. Prophet(log1p) is not competitive in point forecasting and achieves high nominal interval coverage mainly through very wide prediction intervals. Robustness analyses show that the main ranking patterns are broadly stable to alternative segmentation settings, training-window policies, coverage-stabilized subsamples, and alternative target construction based on cumulative confirmed counts. Overall, the results show that simple baselines remain difficult to outperform in epidemic surveillance data and that horizon-specific rolling evaluation is essential for credible forecast comparison under structural change. Author summaryForecasting infectious disease incidence is difficult when case data change rapidly over time and when reporting systems are still evolving. In this study, I examined how several common statistical forecasting models perform on global daily COVID-19 incidence during the early pandemic. Rather than asking which model is best overall, I focused on whether model ranking changes across forecast horizons and whether those conclusions remain stable under different evaluation choices. I compared simple baselines, including naive, seasonal naive, and drift forecasts, with ARIMA, exponential smoothing, and Prophet models using a rolling-origin benchmark that mimics real-time forecasting. I found that forecast ranking depends strongly on the horizon: drift performed best at 1, 7, and 14 days, while seasonal naive performed best at 3 days. Among the transformed statistical models, ARIMA was more competitive at shorter horizons, whereas exponential smoothing was stronger at longer horizons. I also found that these conclusions remained broadly stable under alternative segmentation settings, training windows, coverage-stabilized subsamples, and target definitions. These results show that simple baselines can remain highly competitive in epidemic surveillance data and that horizon-specific evaluation is essential for fair forecast comparison under structural change.

Background: Atrial fibrillation (AFib) is the most common sustained arrhythmia in the world, imposing a heavy clinical and economic burden on global healthcare systems. Early detection of AFib can reduce mortality and morbidity, while helping to alleviate the growing economic burden of cardiovascular diseases. With the increasing availability of digital health technologies, computational solutions have great potential to support the timely diagnosis of cardiac abnormalities. Objectives: With the increasing availability of electrocardiogram (ECG) data from clinical and wearable devices, manual interpretation has become impractical due to its time-consuming and subjective nature. Existing automated approaches often rely on single classifiers or fixed ensembles that primarily optimize predictive accuracy while neglecting model diversity, which leads to limited robustness and generalization across heterogeneous datasets. Therefore, this study aims to develop a robust and diversity-aware framework for automatic AFib detection that simultaneously improves classification performance and model generalizability. To this end, we propose MOE-ECG, a multi-objective ensemble selection and fusion framework that explicitly optimizes both predictive performance and inter-model diversity for reliable AFib detection from ECG recordings. Methods: The proposed multi-objective ensemble (MOE) framework uses ensemble selection as a bi-objective optimization problem and employs multi-objective particle swarm optimization to identify complementary classifiers from a heterogeneous model pool. Unlike conventional ensembles, it explicitly optimizes both predictive performance and diversity and integrates Dempster-Shafer theory for uncertainty-aware decision fusion. After filtering the ECG signals to remove baseline wander and noise, they were segmented into windows of 20, 60, and 120 heartbeats with 50% overlap. The proposed approach was evaluated over five independent runs to assess its stability and generalization. Fifteen statistical and nonlinear features were obtained from the RR-intervals of the pre-processed ECG signals, of which eight features were selected with correlation analysis to capture subtle information from the ECG data. We trained and evaluated the performance of the proposed model in three open source databases, namely, the MIT-BIH Atrial Fibrillation Database, Saitama Heart Database Atrial Fibrillation, and Long-Term AF Database. Results: The proposed approach achieved the best overall performance on 60-beat segments, with an average accuracy of 89.85%, precision of 91.14%, recall of 94.19%, an F1-score of 92.64%, and area under the curve (AUC) of around 0.95. Statistical analysis using Holm-adjusted Wilcoxon tests confirmed significant improvements (p<0.05) compared to both the best individual classifier and the unoptimized average ensemble of all classifiers. These findings show that the proposed selection and evaluation methodology, rather than group aggregation alone, is the key driver of performance improvements. Conclusion: The results obtained demonstrate that the MOE-ECG model offers a robust, accurate, and reliable solution for the detection of AFib from short ECG segments. The empirical findings, in general, confirm that multi-objective ensemble fusion enhances diagnostic performance and offers robust predictions that will open up possibilities for real-time AFib detection in clinical and tele-health settings.

Mental health challenges among university students have increased due to academic pressure, lifestyle changes, and continuous digital engagement. Existing approaches for mental health assessment often rely either on self-reported psychological scales or isolated behavioral indicators, limiting their ability to capture complex temporal and contextual patterns. This study proposes an interpretable multimodal framework for student mental health risk assessment using behavioral sensing, academic information, ecological momentary assessments (EMA), and psychometric survey data. A bidirectional Long Short-Term Memory autoencoder is employed to learn latent temporal representations from day-level behavioral sequences, while graph embeddings capture structural relationships among students using similarity-based neighborhood graphs. These representations are fused with academic and survey-derived features and reduced using Principal Component Analysis and Uniform Manifold Approximation and Projection. K-means clustering is then applied to identify behaviorally distinct student groups. Experimental analysis on the StudentLife dataset demonstrates meaningful clustering performance with a Silhouette Score of 0.4209 and Adjusted Rand Index stability of 0.6869. The identified clusters correspond to low-risk, moderate-risk, and high-risk behavioral profiles. To improve interpretability and practical usability, a fuzzy inference system is introduced to compute mental risk, academic risk, and wellbeing indices using psychometric indicators including PHQ-9, PSS, PANAS, VR-12, and Big Five personality traits. The results demonstrate the potential of combining multimodal behavioral modeling with interpretable fuzzy reasoning to support early mental health risk assessment in educational settings.

AO_SCPLOWBSTRACTC_SCPLOWOncolytic viruses provide cancer therapy using replication-competent viruses that selectively infect and lyse tumour cells. Their tumour-specific replication also enables the delivery of targeted, virus-encoded gene products, such as enzymes that activate prodrugs. This dual functionality offers the potential for synergistic effects by combining direct oncolysis with localised drug activation. The interplay between infection, replication, lysis, and gene product delivery remains poorly understood. Here, we introduce a spatially structured, multi-patch model of cancer cells infected by an oncolytic virus engineered to deliver a prodrug-activating enzyme. The spatial system is first represented as a microscopic model and subsequently reduced via spectral dimension reduction techniques. This reduction yields an ordinary differential equation model for a set of coarse-grained variables, which we analyze both without the transgene (OV model) and with the transgene (TOV model). For each case, we compute the basic reproduction number, R0, which determines the conditions for viral spread. Both models exhibit three regimes via transcritical bifurcations: (i) R0 < 0, extinction of both cancer and infected cells; (ii) 0 < R0 [&le;] 1, persistence of cancer cells only; and (iii) R0 > 1, coexistence as a stable node or as a focus. The TOV model, as a difference form the OV model, can undergo periodic oscillations arising from a Hopf-Andronov bifurcation. Notably, oscillation amplitudes can be controlled such that cancer cells largely decrease when drug-induced death is stronger in non-infected cells than in infected ones, enabling effective cancer cells killing while maintaining viral replication and prodrug activation. The qualitative behaviour of the coarse-grained model is shown to be preserved in both the microscopic and spatially explicit models.

Routine ICU data offers valuable insights into daily physiological rhythms. While traditional methods assume these cycles maintain fixed periods and amplitudes, their inherent variability requires dynamic estimation of instantaneous trends. Wavelet transform effectively resolves circadian oscillations, especially for frequently measured vital parameters. We present novel extensions to the Continuous Wavelet Transform (CWT) power spectral analysis to better detect and segment subtle temporal patterns. Using this approach, we uncover hidden circadian patterns in cardiovascular vitals such as Heart Rate (HR) and Mean Blood Pressure (MBP) measured over five days in a retrospective cohort of 855 ICU patients. By quantifying non-stationary rhythms, we identified diurnal and semi-diurnal oscillations varying in period and power according to delirium and deep sedation. Notably, HR exhibits a clear diurnal and semi-diurnal rhythm when delirium is absent. Overall, our framework supports the CWT as a powerful tool for analyzing complex physiological signals, particularly vital signs. Crucially, our findings suggest that cardiovascular rhythm disruption can be associated with ICU-related delirium and deep sedation.