Data-driven Mathematical Modeling Research Articles

Patient visit behaviour shapes the virus infection dynamics in hosts

Chronic HBV infection is a dynamic process of rapid viral replication and clearance, with large amounts of virus being produced and lost in the body daily. The patient's visit behaviour is closely related to viral load in the body, while the data-driven mathematical model still lacking. Therefore, we first include 28,912 patients to investigate the relationships between the visit behaviour and the HBV-DNA virus load. Then, we propose an HBV virus infection dynamics model that considers the patient's visit behaviour. The system is chaotic once the behaviour of patients during visits depends on the virus load. Our results may help us understand the process of viral transmission, and increasing the visit probability to the clinic can lead to stabilising HBV-DNA viral loads and further help healthcare professionals develop targeted clinical intervention strategies.

Optimized patient-specific immune checkpoint inhibitor therapies for cancer treatment based on tumor immune microenvironment modeling.

Enhancing patient response to immune checkpoint inhibitors (ICIs) is crucial in cancer immunotherapy. We aim to create a data-driven mathematical model of the tumor immune microenvironment (TIME) and utilize deep reinforcement learning (DRL) to optimize patient-specific ICI therapy combined with chemotherapy (ICC). Using patients' genomic and transcriptomic data, we develop an ordinary differential equations (ODEs)-based TIME dynamic evolutionary model to characterize interactions among chemotherapy, ICIs, immune cells, and tumor cells. A DRL agent is trained to determine the personalized optimal ICC therapy. Numerical experiments with real-world data demonstrate that the proposed TIME model can predict ICI therapy response. The DRL-derived personalized ICC therapy outperforms predefined fixed schedules. For tumors with extremely low CD8 + T cell infiltration ('extremely cold tumors'), the DRL agent recommends high-dosage chemotherapy alone. For tumors with higher CD8 + T cell infiltration ('cold' and 'hot tumors'), an appropriate chemotherapy dosage induces CD8 + T cell proliferation, enhancing ICI therapy outcomes. Specifically, for 'hot tumors', chemotherapy and ICI are administered simultaneously, while for 'cold tumors', a mid-dosage of chemotherapy makes the TIME 'hotter' before ICI administration. However, in several 'cold tumors' with rapid resistant tumor cell growth, ICC eventually fails. This study highlights the potential of utilizing real-world clinical data and DRL algorithm to develop personalized optimal ICC by understanding the complex biological dynamics of a patient's TIME. Our ODE-based TIME dynamic evolutionary model offers a theoretical framework for determining the best use of ICI, and the proposed DRL agent may guide personalized ICC schedules.

Real-time assessment of mitochondrial DNA heteroplasmy dynamics at the single-cell level.

Mitochondrial DNA (mtDNA) is present in multiple copies within cells and is required for mitochondrial ATP generation. Even within individual cells, mtDNA copies can differ in their sequence, a state known as heteroplasmy. The principles underlying dynamic changes in the degree of heteroplasmy remain incompletely understood, due to the inability to monitor this phenomenon in real time. Here, we employ mtDNA-based fluorescent markers, microfluidics, and automated cell tracking, to follow mtDNA variants in live heteroplasmic yeast populations at the single-cell level. This approach, in combination with direct mtDNA tracking and data-driven mathematical modeling reveals asymmetric partitioning of mtDNA copies during cell division, as well as limited mitochondrial fusion and fission frequencies, as critical driving forces for mtDNA variant segregation. Given that our approach also facilitates assessment of segregation between intact and mutant mtDNA, we anticipate that it will be instrumental in elucidating the mechanisms underlying the purifying selection of mtDNA.

Rightful Rewards: Refining Equity in Team Resource Allocation through a Data-Driven Optimization Approach

In group management, accurate assessment of individual performance is crucial for the fair allocation of resources such as bonuses. This paper explores the complexities of gauging each participant’s contribution in multi-participant projects, particularly through the lens of self-reporting—a method fraught with the challenges of under-reporting and over-reporting, which can skew resource allocation and undermine fairness. Addressing the limitations of current assessment methods, which often rely solely on self-reported data, this study proposes a novel equitable allocation policy that accounts for inherent biases in self-reporting. By developing a data-driven mathematical optimization model, we aim to more accurately align resource allocation with actual contributions, thus enhancing team efficiency and cohesion. Our computational experiments validate the proposed model’s effectiveness in achieving a more equitable allocation of resources, suggesting significant implications for management practices in team settings.

Data-driven mathematical modeling of sleep consolidation in early childhood

Across early childhood development, sleep behavior transitions from a biphasic pattern (a daytime nap and nighttime sleep) to a monophasic pattern (only nighttime sleep). The transition to consolidated nighttime sleep, which occurs in most children between 2- and 5-years-old, is a major developmental milestone and reflects interactions between the developing homeostatic sleep drive and circadian system. Using a physiologically-based mathematical model of the sleep-wake regulatory network constrained by observational and experimental data from preschool-aged participants, we analyze how developmentally-mediated changes in the homeostatic sleep drive may contribute to the transition from napping to non-napping sleep patterns. We establish baseline behavior by identifying parameter sets that model typical 2-year-old napping behavior and 5-year-old non-napping behavior. Then we vary six model parameters associated with the dynamics of and sensitivity to the homeostatic sleep drive between the 2-year-old and 5-year-old parameter values to induce the transition from biphasic to monophasic sleep. We analyze the individual contributions of these parameters to sleep patterning by independently varying their age-dependent developmental trajectories. Parameters vary according to distinct evolution curves and produce bifurcation sequences representing various ages of transition onset, transition durations, and transitional sleep patterns. Finally, we consider the ability of napping and non-napping light schedules to reinforce napping or promote a transition to consolidated sleep, respectively. These modeling results provide insight into the role of the homeostatic sleep drive in promoting interindividual variability in developmentally-mediated transitions in sleep behavior and lay foundations for the identification of light- or behavior-based interventions that promote healthy sleep consolidation in early childhood.

Avoidance, confusion or solitude? Modelling how noise pollution affects whale migration

Many baleen whales are renowned for their acoustic communication. Under pristine conditions, this communication can plausibly occur across hundreds of kilometres. Frequent vocalisations may allow a dispersed migrating group to maintain contact, and therefore benefit from improved navigation via the “wisdom of the crowd”. Human activities have considerably inflated ocean noise levels. Here we develop a data-driven mathematical model to investigate how ambient noise levels may inhibit whale migration. Mathematical models allow us to simultaneously simulate collective whale migration behaviour, auditory cue detection, and noise propagation. Rising ambient noise levels are hypothesised to influence navigation through three mechanisms: (i) diminished communication space; (ii) reduced ability to hear external sound cues and; (iii) triggering noise avoidance behaviour. Comparing pristine and current soundscapes, we observe navigation impairment that ranges from mild (increased journey time) to extreme (failed navigation). Notably, the three mechanisms induce qualitatively different impacts on migration behaviour. We demonstrate the model’s potential predictive power, exploring the extent to which migration may be altered under future shipping and construction scenarios.

Sliding mode control for gasifier reactor temperature control

This paper presents a sliding mode control (SMC) design for gasifier reactor temperature control. Temperature control is a critical aspect of biomass gasification for quality syngas production. However, accurate modeling and effective control method are the major challenges of gasifier reactor temperature control. The gasification system processes are not yet well understood to model from the first principle due to the complex and nonlinear nature of the process. Also, conventional control methods such as proportional, integral, and derivative control have not been effective in controlling gasification systems. Hence, this work has used experimental data from a 500 kVA updraft gasifier reactor to develop a data-driven mathematical model. The system identification result predicts 86.36% goodness of fit on the model data and 88.26% on the validation data. Discrete time sliding mode control has been designed from the model and implemented in Simulink to investigate the performance of the control method on the gasifier. The result of the system time response shows that the controller effectively drives the temperature monotonically from 25°C to 700 °C in finite time (11.37 minutes). It also establishes a quasi-sliding motion with an ultimate band of ±1℃ for the remainder of the simulation time. Hence, the control technique guarantees optimal temperature control for any feedstock type which will result in higher conversion efficiency, more syngas yield, and improve syngas quality and durability of the gasifier reactor among others.

Model-based evaluation of admission screening strategies for the detection and control of carbapenemase-producing Enterobacterales in the English hospital setting

BackgroundGlobally, detections of carbapenemase-producing Enterobacterales (CPE) colonisations and infections are increasing. The spread of these highly resistant bacteria poses a serious threat to public health. However, understanding of CPE transmission and evidence on effectiveness of control measures is severely lacking. This paper provides evidence to inform effective admission screening protocols, which could be important in controlling nosocomial CPE transmission.MethodsCPE transmission within an English hospital setting was simulated with a data-driven individual-based mathematical model. This model was used to evaluate the ability of the 2016 England CPE screening recommendations, and of potential alternative protocols, to identify patients with CPE-colonisation on admission (including those colonised during previous stays or from elsewhere). The model included nosocomial transmission from colonised and infected patients, as well as environmental contamination. Model parameters were estimated using primary data where possible, including estimation of transmission using detailed epidemiological data within a Bayesian framework. Separate models were parameterised to represent hospitals in English areas with low and high CPE risk (based on prevalence).ResultsThe proportion of truly colonised admissions which met the 2016 screening criteria was 43% in low-prevalence and 54% in high-prevalence areas respectively. Selection of CPE carriers for screening was improved in low-prevalence areas by adding readmission as a screening criterion, which doubled how many colonised admissions were selected. A minority of CPE carriers were confirmed as CPE positive during their hospital stay (10 and 14% in low- and high-prevalence areas); switching to a faster screening test pathway with a single-swab test (rather than three swab regimen) increased the overall positive predictive value with negligible reduction in negative predictive value.ConclusionsUsing a novel within-hospital CPE transmission model, this study assesses CPE admission screening protocols, across the range of CPE prevalence observed in England. It identifies protocol changes—adding readmissions to screening criteria and a single-swab test pathway—which could detect similar numbers of CPE carriers (or twice as many in low CPE prevalence areas), but faster, and hence with lower demand on pre-emptive infection-control resources. Study findings can inform interventions to control this emerging threat, although further work is required to understand within-hospital transmission sources.

A data-driven mathematical model to design a responsive-sustainable pharmaceutical supply chain network: a Benders decomposition approach

A data-driven mathematical model to design a responsive-sustainable pharmaceutical supply chain network: a Benders decomposition approach

Dynamical modeling the effect of glucagon-like peptide on glucose–insulin regulatory system based on mice experimental observation

As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose–insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose–insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.

Variable screening methods in spatial infectious disease transmission models

Data-driven mathematical modelling can enrich our understanding of infectious disease spread enormously. Individual-level models of infectious disease transmission allow the incorporation of different individual-level covariates, such as spatial location, vaccination status, etc. This study aims to explore and develop methods for fitting such models when we have many potential covariates to include in the model. The aim is to enhance the performance and interpretability of models and ease the computational burden of fitting these models to data. We have applied and compared multiple variable selection methods in the context of spatial epidemic data. These include a Bayesian two-stage least absolute shrinkage and selection operator (Lasso), forward and backward stepwise selection based on the Akaike information criterion (AIC), spike-and-slab priors, and random variable selection (boosting) methods. We discuss and compare the performance of these methods via simulated datasets and UK 2001 foot-and-mouth disease data. While comparing the variable selection methods all performed consistently well except the two-stage Lasso. We conclude that the spike-and-slab prior method is to be recommended, consistently resulting in high accuracy and short computational time.

Distribution modeling quantifies collective TH cell decision circuits in chronic inflammation.

Immune responses are tightly regulated by a diverse set of interacting immune cell populations. Alongside decision-making processes such as differentiation into specific effector cell types, immune cells initiate proliferation at the beginning of an inflammation, forming two layers of complexity. Here, we developed a general mathematical framework for the data-driven analysis of collective immune cell dynamics. We identified qualitative and quantitative properties of generic network motifs, and we specified differentiation dynamics by analysis of kinetic transcriptome data. Furthermore, we derived a specific, data-driven mathematical model for T helper 1 versus T follicular helper cell-fate decision dynamics in acute and chronic lymphocytic choriomeningitis virus infections in mice. The model recapitulates important dynamical properties without model fitting and solely by using measured response-time distributions. Model simulations predict different windows of opportunity for perturbation in acute and chronic infection scenarios, with potential implications for optimization of targeted immunotherapy.

Unequal effects of SARS-CoV-2 infections: model of SARS-CoV-2 dynamics in Cameroon (Sub-Saharan Africa) versus New York State (United States)

Worldwide, the recent SARS-CoV-2 virus disease outbreak has infected more than 691,000,000 people and killed more than 6,900,000. Surprisingly, Sub-Saharan Africa has suffered the least from the SARS-CoV-2 pandemic. Factors that are inherent to developing countries and that contrast with their counterparts in developed countries have been associated with these disease burden differences. In this paper, we developed data-driven COVID-19 mathematical models of two ‘extreme’: Cameroon, a developing country, and New York State (NYS) located in a developed country. We then identified critical parameters that could be used to explain the lower-than-expected COVID-19 disease burden in Cameroon versus NYS and to help mitigate future major disease outbreaks. Through the introduction of a ‘disease burden’ function, we found that COVID-19 could have been much more severe in Cameroon than in NYS if the vaccination rate had remained very low in Cameroon and the pandemic had not ended.

Research on online interactive identification method for motion model of double propeller propulsion unmanned surface vehicle based on ESO disturbance estimation

In this paper, the online parameter identification problem of the mathematical model of USV considering the characteristics of the actuator is studied. A data-driven mathematical model of motion is very meaningful to realize trajectory prediction and adaptive motion control of USV. An interactive identification algorithm (ESO-MILS) based on Extended State Observer (ESO) is proposed. The robustness of online identification is improved by expanding the state observer to estimate the current disturbance without making artificial assumptions. Specifically, the three-degree-of-freedom dynamic equation of the double propeller propulsion USV is constructed. A linear model for online identification is derived by parameterization. Based on the least square criterion function, it is proved that the interactive identification method with disturbance estimation can improve the identification accuracy from the perspective of mathematical expectation. The extended state observer is designed to estimate the unknown disturbance in the model. The online interactive update improves the disturbance immunity of the identification algorithm. Finally, the effectiveness of the interactive identification algorithm is verified by simulation experiment and real ship experiment.

Dynamic recycling of extracellular ATP in human epithelial intestinal cells.

Intestinal epithelial cells play important roles in the absorption of nutrients, secretion of electrolytes and food digestion. The function of these cells is strongly influenced by purinergic signalling activated by extracellular ATP (eATP) and other nucleotides. The activity of several ecto-enzymes determines the dynamic regulation of eATP. In pathological contexts, eATP may act as a danger signal controlling a variety of purinergic responses aimed at defending the organism from pathogens present in the intestinal lumen. In this study, we characterized the dynamics of eATP on polarized and non-polarized Caco-2 cells. eATP was quantified by luminometry using the luciferin-luciferase reaction. Results show that non-polarized Caco-2 cells triggered a strong but transient release of intracellular ATP after hypotonic stimuli, leading to low micromolar eATP accumulation. Subsequent eATP hydrolysis mainly determined eATP decay, though this effect could be counterbalanced by eATP synthesis by ecto-kinases kinetically characterized in this study. In polarized Caco-2 cells, eATP showed a faster turnover at the apical vs the basolateral side. To quantify the extent to which different processes contribute to eATP regulation, we created a data-driven mathematical model of the metabolism of extracellular nucleotides. Model simulations showed that eATP recycling by ecto-AK is more efficient a low micromolar eADP concentrations and is favored by the low eADPase activity of Caco-2 cells. Simulations also indicated that a transient eATP increase could be observed upon the addition of non-adenine nucleotides due the high ecto-NDPK activity in these cells. Model parameters showed that ecto-kinases are asymmetrically distributed upon polarization, with the apical side having activity levels generally greater in comparison with the basolateral side or the non-polarized cells. Finally, experiments using human intestinal epithelial cells confirmed the presence of functional ecto-kinases promoting eATP synthesis. The adaptive value of eATP regulation and purinergic signalling in the intestine is discussed.

Hybrid discrete-time-continuous-time models and a SARS CoV-2 mystery: Sub-Saharan Africa's low SARS CoV-2 disease burden.

Worldwide, the recent SARS-CoV-2 virus has infected more than 670 million people and killed nearly 67.0 million. In Africa, the number of confirmed COVID-19 cases was approximately 12.7 million as of January 11, 2023, that is about 2% of the infections around the world. Many theories and modeling techniques have been used to explain this lower-than-expected number of reported COVID-19 cases in Africa relative to the high disease burden in most developed countries. We noted that most epidemiological mathematical models are formulated in continuous-time interval, and taking Cameroon in Sub-Saharan Africa, and New York State in the USA as case studies, in this paper we developed parameterized hybrid discrete-time-continuous-time models of COVID-19 in Cameroon and New York State. We used these hybrid models to study the lower-than-expected COVID-19 infections in developing countries. We then used error analysis to show that a time scale for a data-driven mathematical model should match that of the actual data reporting.

Exploring computer-aided health decision-making on cervical cancer interventions through deliberative interviews in Ethiopia

Cervical cancer is a significant disease burden in Ethiopia. Mathematical models and computer simulations on disease dynamics can support effective resource allocation. The objectives of this work are (i) to explore the perspectives of health decision-makers on computer-aided predictions supporting cervical cancer interventions, (ii) to identify their information needs from these predictions, and (iii) their willingness to apply the results in their work. We conducted deliberative interviews with 15 health decision-makers and advisors in Ethiopia in autumn 2019. We analyze the data using a five steps framework approach drawing on thematic analysis and find that Ethiopian health decision-makers are willing to use computer-aided predictions in their decisions. Data on HPV prevalence and the cervical cancer burden are scarce but valued highly and decision-makers are particularly interested in the identification of local HPV hotspots. Data-driven mathematical models and computer simulations may increasingly influence health decision-making in Ethiopia.

Dynamics of CLIMP-63 S-acylation control ER morphology

The complex architecture of the endoplasmic reticulum (ER) comprises distinct dynamic features, many at the nanoscale, that enable the coexistence of the nuclear envelope, regions of dense sheets and a branched tubular network that spans the cytoplasm. A key player in the formation of ER sheets is cytoskeleton-linking membrane protein 63 (CLIMP-63). The mechanisms by which CLIMP-63 coordinates ER structure remain elusive. Here, we address the impact of S-acylation, a reversible post-translational lipid modification, on CLIMP-63 cellular distribution and function. Combining native mass-spectrometry, with kinetic analysis of acylation and deacylation, and data-driven mathematical modelling, we obtain in-depth understanding of the CLIMP-63 life cycle. In the ER, it assembles into trimeric units. These occasionally exit the ER to reach the plasma membrane. However, the majority undergoes S-acylation by ZDHHC6 in the ER where they further assemble into highly stable super-complexes. Using super-resolution microscopy and focused ion beam electron microscopy, we show that CLIMP-63 acylation-deacylation controls the abundance and fenestration of ER sheets. Overall, this study uncovers a dynamic lipid post-translational regulation of ER architecture.

Selecting slacks-based data envelopment analysis models

Data envelopment analysis (DEA) is a well-known data-driven mathematical modeling approach that aims at evaluating the relative efficiency of a set of comparable decision making units (DMUs) with multiple inputs and multiple outputs. The number of inputs and outputs (performance factors) plays a vital role for successful applications of DEA. There is a statistical and empirical rule in DEA that if the number of performance factors is high in comparison with the number of DMUs, then a large percentage of the units will be determined as efficient, which is questionable and unacceptable in the performance evaluation context. However, in some real-world applications, the number of performance factors is relatively larger than the number of DMUs. To cope with this issue, selecting models have been developed to select a subset of performance factors that lead to acceptable results.In this paper, we extend a pair of optimistic and pessimistic approaches, involving two alternative individual and summative selecting models, based on the slacks-based model. We mathematically validate the proposed models with some theorems and lemmas and illustrate the applicability of our models using 18 active auto part companies in the largest stock exchange in Iran.

Modulation of signaling cross-talk between pJNK and pAKT generates optimal apoptotic response.

Tumor necrosis factor alpha (TNFα) is a well-known modulator of apoptosis by maintaining a balance between proliferation and cell-death in normal cells. Cancer cells often evade apoptotic response following TNFα stimulation by altering signaling cross-talks. Thus, varying the extent of signaling cross-talk could enable optimal TNFα mediated apoptotic dynamics. Herein, we use an experimental data-driven mathematical modeling to quantitate the extent of synergistic signaling cross-talk between the intracellular entities phosphorylated JNK (pJNK) and phosphorylated AKT (pAKT) that orchestrate the phenotypic apoptosis level by modulating the activated Caspase3 dynamics. Our study reveals that this modulation is orchestrated by the distinct dynamic nature of the synergism at early and late phases. We show that this synergism in signal flow is governed by branches originating from either TNFα receptor and NFκB, which facilitates signaling through survival pathways. We demonstrate that the experimentally quantified apoptosis levels semi-quantitatively correlates with the model simulated Caspase3 transients. Interestingly, perturbing pJNK and pAKT transient dynamics fine-tunes this accumulated Caspase3 guided apoptotic response. Thus, our study offers useful insights for identifying potential targeted therapies for optimal apoptotic response.