Mathematics

Neural temporal point processes (NTPPs) are powerful tools for modeling sequences of timestamped events with statistical temporal structure. Density-based NTPPs, in particular, are an interesting opportunity to merge the universal function approximation capability of neural networks with a defined statistical model in a way that has many potential applications. We demonstrate one such application to heartbeat dynamics, a physiologic point process. We specifically apply a lognormal mixture NTPP to compute instantaneous estimates of the mean and standard deviation of beat-to-beat intervals. We compare our results to the state of art (Barbieri et al.) point process model for heartbeat dynamics, which uses a more physiologically rigorous inverse Gaussian model. We find that the NTPP model maintains reasonable accuracy while improving upon robustness to noise.

We present a quantum-enhanced version of the classic k-Nearest Neighbors (kNN) classification algorithm, applied to the prediction of arterial hypertension. The traditional Euclidean distance metric of the kNN algorithm is replaced with a Fidelity-derived quantum dissimilarity measure to evaluate the similarity between data samples. We map classical real-world clinical and ECG-derived data features into quantum states via the Dense-Angle Encoding, which efficiently utilizes parameterized rotation gates to pack multiple features into minimal qubits while maintaining pure states. We evaluate the performance of the dissimilarity measure using both the noiseless state vector Simulator and the IBM Qiskit Estimator primitives. The quantum circuit demonstrates robust predictive capabilities comparable to the classical model. While it does not claim computational supremacy over the classical baseline, the framework proves that fidelity-based similarity is a physically meaningful and efficient approach for hybrid quantum classical classification.

Infectious disease transmission evolves as a dynamic process shaped by biological mechanisms, population behavior, and intervention policies, yet public health responses are often driven by lagging indicators. Accurate short- and long-term disease forecasting is essential for the timely deployment of intervention strategies, healthcare capacity planning, and uncertainty-aware, risk-informed decision-making. To address this challenge, three broad classes of forecasting models have traditionally been used: statistical, machine learning, and mechanistic approaches. However, each of these modeling paradigms faces fundamental limitations. In particular, traditional statistical models often lack the flexibility needed to capture complex disease dynamics, machine learning approaches require large, high-quality data streams, and mechanistic models are notoriously difficult to calibrate. To overcome these challenges, we propose a novel physics-informed machine learning (PIML) framework for forecasting infectious disease dynamics. Our approach simultaneously forecasts new case and hospitalization counts, along with other key epidemiological quantities such as the time-varying reproduction number. This is achieved through the design of a machine learning model and estimation strategy regularized by a system of differential equations that encode disease dynamics of the SIHR model, thereby bridging the gap between purely data-driven and mechanistic models. We demonstrate the proposed methodology through in-depth numerical studies and an application to COVID-19 data collected in the state of South Carolina.

Length and time constants are foundational to the study of conduction in neurons and other biological cables but are exactly defined only for passive membranes. Here we define and derive exact length and time constants for propagating action potentials in unmyelinated axons. This derivation exploits specific instants during action potential conduction when the net transmembrane ionic current is zero, but axial current remains non-zero. At these instants, we define a curvature parameter,{kappa} , explore its determinants using computer modelling, demonstrate that it is the local real Laplace exponent of the action potential upstroke, and suggest practical approaches for its experimental measurement. From{kappa} , we define action potential length and time constants, {lambda}AP = 1/{surd}({kappa}racm) and {tau}AP = 1/{kappa}, and show that action potential propagation velocity is exactly {lambda}AP/{tau}AP.

The initial response of populations to the SARS-CoV-2 virus reduced the incidence of COVID-19 cases. However, this success was shorted lived once most populations relaxed most restrictions, resulting in an increase in infections. This feedback contributed to additional pandemic waves. The temporal unfolding of behavioural changes in populations present a challenge to mathematical models for disease dynamics. Coupled behaviour-disease models with varying levels of complexity accounting for several factors have been used to capture behavioural dynamics and SARS-CoV-2 transmission, with varying results. To study the impact of model complexity on the predictive power of models, here we formulate five coupled behaviour-disease models with varying structure and number of parameters. We fit the models to SARS-CoV-2 infection incidence and stringency of control interventions from five European countries in the first wave, and study how well these fitted models predict the second wave. We show that models with more parameters do not necessarily have a greater ability to explain and predict key features of a pandemic wave. Hence, our results show that a relatively simple coupled behaviour-disease model with important parameters can do an adequate job of providing information about the pandemic wave. Additionally, our findings show that complex models can be country-specific, working better for some countries and poorly for others. We conclude that modellers should not always opt for the most complicated possible models, if the data do not support their use.

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

Scaling laws help determine the optimal data size for training large models but are established in domains where the target is deterministic. Physiological signals are different: heartbeat sequences are stochastic, so part of the error is irreducible even with large amounts of data. Metrics such as MAE do not account for non-deterministic behavior, and therefore assessing scaling requires evaluating distributional calibration (measuring how well predicted probability densities capture true conditional characteristics). We formulate a scaling law metric(n) = E + A n- and evaluate it with five metrics: accuracy (MAE, RMSE), distributional calibration (KS distance, goodness-of-fit), and training objective (negative log loss) using a neural temporal point process trained on a cohort of four-ECG datasets. The law fits all five metrics. While point accuracy is near saturation at n = 183, KS distance and goodness-of-fit improve by 6% and 12% respectively when extrapolated to 10,000 subjects, showing that scaling decisions in stochastic domains must be guided by distributional calibration rather than point accuracy.

AO_SCPLOWBSTRACTC_SCPLOWIn this work, we publish the 3D unsteady Navier-Stokes numerical simulations and meshes of coronary arteries reconstructed from invasive X-ray coronary angiograms acquired during in the Fractional Flow Reserve versus Angiography for Multivessel Evaluation 2 (FAME 2) trial. Out of the 914 clinical images, 779 vessels are successfully reconstructed and meshed. The remaining 135 vessels have been discarded since they exhibited self-intersecting geometry during the reconstruction process. The meshes are hexahedral and all of them have the same number of vertices and identical connectivity; their high quality is demonstrated using standard mesh quality indices. The simulations are performed using the Finite Element Method (FEM) with state-of-the-art coronary boundary conditions applied at the outlet. The motivation behind this effort relies from the scarcity of publicly available numerical haemodynamics data, despite the growing interest in data-driven modeling and machine learning techniques. The database is available at the link: https://doi.org/10.7910/DVN/GPCUNS

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Clinical decisions for determining optimal patient-specific interventions are complicated prediction tasks that rely on health care professionals' understanding of physiological mechanisms and their dynamics. These decisions are challenged by (a) observational data sparsity and (b) patient heterogeneity. Here, we focus on estimating and forecasting specific physiological properties--that are not explicitly present in clinical observations--to provide additional features using only data available bedside at the time of decision-making. Mechanistic models of physiological system(s), e.g., physiological ordinary differential equation (ODE) models, provide pathways to compensate for data sparsity by synchronizing the model with observations of an individual patient using data assimilation (DA). However, DA used in a standard computational workflow to estimate constant model parameters from presently-known data is less effective at optimizing state forecasts of the model governed by physiological processes that evolve before new observations are available. Stated simply, we cannot forecast the future evolution of the model because we cannot forecast model parameters. To support next-generation clinical decision support, we develop a new DA and machine learning (ML) hybrid pipeline to estimate and forecast individual future physiological processes by forecasting ODE model parameters. This pipeline overcomes model and DA workflow limitations by stacking a DA-estimated posterior empirical distribution of physiological parameters with longitudinal ML forecasting models. We work within the context of glycemic management in an ICU using EHR data to construct and test a use case. We use synthetic data and real-world clinical data to validate the integrated pipeline and quantify uncertainties.

High pathogenicity avian influenza (HPAI) H5N1 clade 2.3.4.4b has caused a global panzootic with unprecedented impacts on wildlife and livestock, making evidence-based disease mitigation and outbreak response critical. In this paper, we describe a spatiotemporal mechanistic model of infectious disease dynamics developed for the HPAI Modelling Challenge and its implications for forecasting and policy in Australia. To emulate emergency response conditions, we adapted an existing model for rapid deployment rather than developing a bespoke model. We refined the model iteratively across the challenge to better analyse the provided outbreak data. Throughout the challenge, we accurately forecast temporal trends and local outbreak spread, but could not predict rarer, long-distance dispersal events. The challenge ended before HPAI H5N1 was first detected in Australia (June 2026), providing a critical opportunity to test our response modelling readiness for an incursion in wildlife and potential spillover into commercial poultry. Our experience identifies three key considerations for Australia's HPAI H5N1 preparedness: targeted enhancements to our model to improve forecast precision and enable scenario-based policy evaluation; the critical value of pre-existing modelling infrastructure for rapid emergency response; and sustained collaboration between research and policy institutions to align modelling capabilities with outbreak response requirements.

Chronic wounds (principally pressure sores, venous leg ulcers and diabetic foot ulcers) are a drain on global health services and remain a major area of unmet clinical need. Chronic wounds are characterised by a bacterial biofilm (densely aggregated colonies of bacteria encased by a matrix of extracellular polymeric substances), which hinders innate immune response and can prevent wound healing. Bioactive glass (BG) fibres doped with antimicrobial metal ions, such as silver, can offer a promising treatment for chronic wound infections, where silver is well known for its antimicrobial activity against a range of pathogens and is commonly used in wound dressings. We first present a system of non-linear partial differential equations to model the treatment of a chronic wound biofilm infection with BG fibres. The BG fibres are assumed to have two mechanisms of action against the biofilm: physical disruption of the top layers of the biofilm by the BG fibres; and release of antimicrobial silver ions from the BG fibres, which then diffuse into the biofilm and can kill the bacteria. Treatment-associated parameters are estimated from in vitro experimental data using a combination of least-squares minimisation and Approximate Bayesian Computation (ABC). Sensitivity investigations are performed on other parameters that cannot currently be calculated experimentally to investigate their influence on treatment efficacy. We thus predict key parameter regimes that should lead to biofilm eradication, crucially informing the future design of metal-doped BG fibres to maximise treatment efficacy. Author summaryChronic wounds are a huge drain on global health services and will become even more problematic due to an ageing population. Current treatment methods are often unsuccessful, where treatment failure is exacerbated by the presence of a biofilm infection. Biofilms consist of communities of bacteria that adhere to the wound surface and produce extracellular polymeric substances, which can protect the bacteria by acting as both a physical and chemical barrier. More recently, there has been a focus on biofilm-based wound care, where the aim is to firstly eradicate the biofilm infection, which then enables wound healing to occur naturally. Our aim is to produce a novel treatment that can target and eradicate the biofilm infection, followed by directly assisting the wound healing. Bioactive glass (BG) fibres doped with silver offer a promising treatment as they have both anti-biofilm effects and can also stimulate the wound healing process. Here, we restrict attention to their anti-biofilm properties. By developing a mathematical model, we can predict treatment outcomes under several different scenarios, the results of which can then be utilised during design of the BG fibres. Using this combination of computational and experimental approaches, we reduce both the cost and time of optimising this promising treatment.

The measurement of light received at the cornea of the eye is a paramount consideration for the understanding of the relation between environmental illumination and the non-image-forming effects of light. The field of view (FOV) at the cornea is less than a full hemisphere, because it is partially occluded by human facial morphology. The International Commission on Illumination (CIE) has defined a standard model of human FOV. A suitably designed physical occluder attached to the sensor (of a light meter) has been proposed as a means of incorporating the effect of human FOV when taking measurements. Similarly, when using simulation to predict light received at the cornea, a geometrical description of the occluder at the eye point(s) can be added to the 3D model of the scene. The first occluder model proposed to represent CIE human FOV was enumerated in terms of: the CIE definition; the radius of the occluder; and, the radius of the light sensor disc. We present a simpler model based only on the CIE definition and the occluder radius. Both models were tested using a virtual goniophotometer. Various sensor response functions describing the spatial sensitivity across the sensor disc, including several we characterized through laboratory measurements, were included in the test. For all functions considered, the performance of the simpler occluder model was equivalent to or better than the model first proposed.

Human Papillomavirus (HPV) infection among men who have sex with men (MSM) has become a significant public health concern, particularly in countries where male vaccination is unavailable. Given the high susceptibility of MSM to HPV and anal cancer, and the unavailability of HPV vaccination for males in low- and middle-income countries (LMICs), there is a need to identify alternative interventions for reducing disease transmission and burden in this population. The novel mathematical model presented in this article couples smoking behavior dynamics with HPV transmission and anal cancer progression among MSM. Smoking reduction is introduced as an intervention to assess its effects on disease transmission and burden. The basic reproduction number (R0) is derived using the next-generation matrix method, and a global sensitivity analysis is performed using partial rank correlation coefficients (PRCC) to identify the influence of model parameters on RR0. Further, the theoretical analysis of the model reveals a backward bifurcation, implying that RR0 < 1 is necessary but not sufficient to eradicate the disease. The study finds that smoking reduction among MSM reduces HPV infection and anal cancer burden relative to baseline projections without intervention. The joint effect of smoking reduction and vaccination shows that the critical vaccination coverage needed to achieve RR0 <1 decreases as the level of smoking reduction increases. A similar outcome is observed for contact reduction. These findings highlight the importance of concurrent interventions, which can significantly curtail the spread of HPV and reduce disease burden in both the high-risk group and the general population.

Breast cancer cells that disseminate to distant organs can remain dormant (non-proliferative) for years before reactivating and progressing into lethal metastatic disease. Understanding the transition between dormancy and reactivation is therefore critical for early intervention and treatment. In this study, we investigate a comprehensive range of deep learning (DL) architectures to classify dormant versus proliferative breast tumor cells within a 3-dimensional growth factor reduced basement membrane extract (3D BME) system that models tumor dormancy and outgrowth. To capture the underlying spatiotemporal dynamics, we evaluate both spatial and sequence-based learning approaches. We consider convolutional neural networks (EfficientNet, ResNet, DenseNet, MobileNet, VGG, AlexNet), segmentation-based models (U-Net, U-Net++, Attention U-Net, DeepLabV3, HRNet) and transformer-based architectures (Vision Transformer, Swin Transformer, SegFormer). We investigate transfer learning using both fixed and fine-tuned strategies. Experimental results show that classification performance is greatly enhanced through the integration of temporal information. EfficientNet-B7, EfficientNet-B6, DenseNet-169, and DenseNet201 are consistently better than competing architectures for all tested models. EfficientNet-B7 with the use of temporal sequences input reaches an accuracy of 98.86% with a ROC-AUC of 0.998. The results highlight the significance of spatio-temporal feature learning and the value of DL frameworks in automated classification of dormant versus proliferative breast cancer cells in physiologically relevant microenvironments.

Fetal-monitoring biomarkers for neonatal hypoxic-ischemic brain injury face a structural gap: the mechanistic ground truth that would label a training set -- perfusion pressure, the moment of decompensation, the injury time course -- cannot be measured at scale or ethically in human pregnancy or labor, and generative synthetic data carry no mechanistic labels. We address this with a mechanistic computational model of the fetal cardiovascular, autonomic, and metabolic response to controlled hypoxic stress, and use it to test how beat detection and acquisition fidelity alter the interpretation of fetal-heart-rate-variability (HRV) biomarkers. The model integrates these systems forward in time across antepartum development (gestational-age growth scaling) and intrapartum stress (umbilical-cord occlusions), emitting synthetic monitoring signals (fetal heart rate, RR intervals) co-registered with model-computed latent labels (pH, base deficit, lactate, perfusion pressure, decompensation and injury states). In a fetal-sheep-derived autonomic-loop configuration we report three results. First, a phase-accumulator beat detector shows that the apparently physiologic baseline HRV of an earlier build was largely a detector artifact, and a noise-off control shows beat-to-beat variability requires an explicit stochastic driver rather than self-sustained autonomic oscillation. Second, a sampling-fidelity sweep yields a fidelity-matched selection rule: a deceleration-area biomarker is preserved at CTG-grade 4 Hz whereas RMSSD is corrupted there (inflated about 8-fold by timing quantization) and recovers only at fetal-ECG rates. Third, autonomic modulation alone does not reproduce the published RMSSD rise-then-collapse -- a negative result that motivates, but does not prove, an intrinsic sinoatrial-pacemaker contribution as a testable hypothesis. This is an in-silico, hypothesis-generating study: the model is not validated for individual fetal prediction, clinical risk estimation, or clinical decision-making. The model is implemented as Fetal Twin (engine fetaltwin), a source-available research instrument released under a noncommercial license, together with all figure configurations, so that these controlled experiments are reproducible. Key PointsO_LIProgress on fetal-monitoring biomarkers for neonatal brain-injury risk is constrained by a structural gap: the mechanistic ground truth that would label a training set -- perfusion pressure, the moment of cardiovascular decompensation, the time course of injury -- cannot be measured at scale or ethically during human pregnancy or labor. C_LIO_LIWe present Fetal Twin (source-available engine fetaltwin), a publicly available, noncommercially-licensed mechanistic testbed for fetal physiological development. It integrates the fetal cardiovascular, metabolic, and autonomic systems forward in time across antepartum development (gestational-age growth scaling) and intrapartum stress (umbilical-cord occlusions), and emits synthetic monitoring signals (fetal heart rate, RR intervals) co-registered with model-computed latent labels (pH, lactate, perfusion pressure, decompensation and injury states). C_LIO_LIThe names digital-twin connotation is deliberate but bounded: Fetal Twin is a mechanistic, population-level twin of fetal physiology used as a research instrument -- not a validated, patient-specific clinical digital twin or predictor. Its purpose is to interrogate what candidate biomarkers can and cannot mean, via in-silico controls impossible in vivo -- swapping the beat detector, turning a noise source off, ablating a reflex, or quantizing the signal to a monitors sampling grid. C_LIO_LIDemonstrations in a fetal-sheep-derived autonomic-loop configuration show that beat-to-beat HRV amplitude can be a numerical artifact of the beat detector, and that in this model class beat-to-beat variability requires an explicit stochastic driver -- it does not arise as a self-sustained oscillation of the deterministic autonomic loop. C_LIO_LIA further demonstration establishes a fidelity-matched biomarker-selection rule -- a deceleration-area biomarker survives CTG-grade 4 Hz sampling whereas RMSSD is corrupted at that rate and needs fetal-ECG timing -- and a negative result shows the published RMSSD "rise-then-collapse" is not reproducible from autonomic modulation in this model class, motivating (but not proving) an intrinsic-pacemaker hypothesis. C_LI

Cancer-associated signaling pathways often exhibit abnormal activation under simultaneous dysregulation of multiple molecular components. This study presents a probabilistic temporal Dynamic Bayesian Network (DBN)-based framework for analyzing multi-fault behaviour and intervention response in Growth Factor (GF) and Mitogen-Activated Protein Kinase (MAPK) signaling pathways. Unlike deterministic Boolean propagation, the proposed model represents each pathway component through an activation probability and propagates these probabilities over discrete time steps using soft-logic update rules. One-, two-, three-, and four-fault scenarios were systematically evaluated under a common lowest-burden input vector. The resulting output probabilities were summarized using an encoded pathway-burden score, and known-drug combinations were ranked using efficiency scores relative to no-intervention baselines. Pareto analysis was further used to balance intervention efficiency against drug-vector burden, while a custom dual-target search was performed to identify computational intervention hypotheses beyond predefined drug targets. Results showed that encoded burden increased with fault order in both pathways, with MAPK producing a higher baseline burden than GF. Among known-drug vectors, U0126+LY294002+Temsirolimus consistently emerged as the strongest low-burden candidate, achieving efficiency close to the maximum six-drug vector. Custom dual-target analysis identified ERK1/2+RPS6KB1 in GF and Raf+MEK1 in MAPK as high-impact computational target pairs. Runtime benchmarking showed that batched vectorized NumPy execution substantially improved scalability for higher-order fault simulations. Overall, the framework provides an interpretable and scalable approach for probabilistic pathway-level fault analysis and intervention prioritization.

The process of medical diagnostics is challenging, especially since patients can simultaneously suffer from several diseases with similar, contradictory, or even opposing diagnoses. Statistical prediction can support physicians in this task; however, the quality of data used for predicition as well as the chosen statistical model can affect the reliability of data-driven decision support. Data quality can, in particular, be reduced by incomplete medical diagnoses, that is, the termination of the diagnostic process once a patient has tested positive for one disease that explains the symptoms. When interpreting missing diagnoses as negative, this leads to potentially false negative health data. Another source of low data quality lies in diagnoses being made through a principle of elimination, i.e., after several negative results, one opts for the seemingly last remaining possibility. This may lead to false positive health data. In our work, we investigate how such inaccurately labeled data affects the predictive ability of multi-label classification (MLC) for disease recognition. Unlike single-label classification (SLC), MLC allows the simultaneous assignment of multiple diseases to a patient and can therefore describe clinical conditions more holistically. To that end, we conduct a synthetic-data simulation study as well as a real-data case study on the example of chronic pain patients. In this regard, we compare MLC performance on accurately and inaccurately labeled data. We manipulate the data such that it corresponds to different diagnostic test sensitivities as well as to different examination sequences, thus paying special attention to resulting uncertainty within the process of medical diagnostics. Our results show that inaccurate labeling substantially decreases MLC prediction ability. Furthermore, low diagnostic test-sensitivity, the order of disease examination and covariate effects have a strong impact on MLC performance. These findings contribute to a better understanding of the interplay and impact of diagnostic procedures, data documentation and interpretation, and statistical modeling. This underlines the need for careful data collection as a basis for model development; special consideration should be given to the extensive examination of patients as well as the targeted collection of covariates. This is particularly crucial when models are transferred into everyday clinical practice.

Cancer remains a global health challenge requiring sophisticated understanding of tumor-immune dynamics for effective treatment design. Mathematical oncology has emerged as a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. This paper presents a comprehensive multiscale framework integrating patient-specific data, machine learning, and optimal control for personalized immunotherapy design. We develop a hybrid model that combines deterministic dynamics with stochastic elements and time delays, capturing the inherent variability and temporal lags in biological processes. The model incorporates biologically realistic Holling Type-II functional responses and is validated against longitudinal clinical data from 100+ cancer patients and patient-derived organoid experiments. Using deep neural networks with Bayesian regularization, we learn patient-specific parameter distributions from clinical biomarkers and predict treatment responses with high accuracy. Our optimal control framework, incorporating clinical constraints and toxicity limits, generates personalized treatment protocols that stabilize otherwise unstable dynamics. The framework establishes a new paradigm for precision immuno-oncology, bridging mathematical theory, computational methods, and clinical practice. Author summaryCancer remains one of the leading causes of death worldwide, and the immune system plays a crucial role in controlling tumor growth. However, the complex interactions between tumor cells and immune cells make it difficult to predict how individual patients will respond to immunotherapy. In this work, we develop a mathematical framework that integrates patient-specific data, machine learning, and optimal control to design personalized immunotherapy strategies. Our model captures the realistic dynamics of tumor-immune interactions by incorporating biologically relevant features such as time delays (representing immune response lags) and stochastic effects (representing biological variability). Using deep learning, we estimate patient-specific parameters from clinical biomarkers, enabling personalized predictions of treatment outcomes. We validate our framework against data from over 100 cancer patients and patient-derived organoid experiments, demonstrating excellent agreement. Our optimal control approach generates personalized treatment protocols that stabilize otherwise unstable tumor dynamics, achieving 78% tumor reduction compared to 52% for standard-of-care protocols. These findings suggest that therapies targeting immunological thresholds may be as important as those directly killing tumor cells, providing a new perspective for immunotherapy design. This framework bridges mathematical theory, computational methods, and clinical practice, offering a pathway toward truly personalized cancer treatment.

Skin cancer requires early detection for improved survival rates. Most existing methods rely on deep learning based image classification, which is affected by visual similarity among lesions. Fewer studies use Gene Expression (GE) analysis, which captures molecular characteristics but lacks structural and visual details. To overcome limitations of individual modalities, this paper proposes a multimodal framework integrating dermoscopic images and GE profiles for skin cancer classification. EfficientNet and logistic regression are used for image based analysis and genomic skin lesion profiling, respectively, followed by fuzzy rule based decision systems to reduce uncertainty within individual modalities. Finally, fuzzy fusion combines predictions from both modalities using uncertainty based weighting of classifier outputs. The experimental findings show that both the image based and GE based classification models individually achieved accuracies of nearly 92%. However, the integration of prediction results through the proposed fuzzy fusion strategy further enhanced the classification performance, achieving an overall accuracy of 94.25%. The results obtained outperform contemporary methods, highlighting the effectiveness of combining complementary multimodal information compared with single modality approaches.