Mathematical Model Research Articles

Proportional population models and stability analysis on time scales

Abstract The study of changes in population size and reasons for these changes appear as population dynamics. These dynamics generally focus on change in population size over time. Mathematical modeling is used to make sense of these changes. In this study, three population models have been reconstructed and solved using proportional derivative on time scales. Equilibrium points and stability states of these solutions were examined.

Methodology of Determining the Intensity of Heat Exchange in a Polytunnel: A Case Study of Synergy Between the Polytunnel and a Stone Heat Accumulator

This paper presents the results of laboratory tests on the intensity of mass and heat exchange in a polytunnel, with a focus on the synergy between the polytunnel and a stone accumulator. The subject of study was a standard polytunnel made of double polythene sheathing. In the process of selecting the appropriate working conditions for such a polytunnel, the characteristic operating parameters were modeled and verified. They were related to the process of mass and energy exchange, which takes place in regular controlled-environment agriculture (CEA). Then, experimental tests of a heat accumulator on a fixed stone bed were carried out. The experiments were carried out for various accumulator surfaces ranging from 18.7 m2 to 74.8 m2, which was measured perpendicularly to the heat medium. To standardize the results obtained, the analysis included the unit area of the accumulator and the unit time of the experiment. In this way, 835 heat and mass exchange events were analyzed, including 437 accumulator charging processes and 398 discharging processes from April to October, which is a standard period of polytunnel use in the Polish climate. During the tests, internal and external parameters of the process were recorded, such as temperature, relative humidity, solar radiation, wind speed and air flow speed in the accumulator system. Based on the parameters, a set of empirical relationships was developed using mathematical modeling. This provided the foundation for calculating heat gains as a result of its storage in a stone accumulator and its discharging process. The research results, including the developed dependencies, not only fill the scientific gap in the field of heat storage, but can also be used in engineering design of polytunnels supported by a heat storage system on a stone bed. In addition, the proposed methodology can be used in the study of other heat accumulators, not only in plant production facilities.

A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanisms.

Ketosis-prone diabetes mellitus (KPD) is a subtype of type 2 diabetes, which presents much like type 1 diabetes, with dramatic hyperglycemia and ketoacidosis. Although KPD patients are initially insulin-dependent, after a few months of insulin treatment, roughly 70% undergo near-normoglycemia remission and can maintain blood glucose without insulin, as in early type 2 diabetes or prediabetes. Here, we propose that these phenomena can be explained by the existence of a fast, reversible glucotoxicity process, which may exist in all people but be more pronounced in those susceptible to KPD. We develop a simple mathematical model of the pathogenesis of KPD, which incorporates this assumption, and show that it reproduces the phenomenology of KPD, including variations in the ability for patients to achieve and sustain remission. These results suggest that a variation of our model may be able to quantitatively describe variations in the course of remission among individuals with KPD.

Evapotranspiration and Crop Coefficient of Green Chives Grown in a Protected Environment

Objective: This study aimed to evaluate the water consumption and reference evapotranspiration (ET₀) of green chives grown in a protected environment using different mathematical models. Theoretical Framework: The present research is based on concepts of plant physiology and irrigation management, both in a protected environment. Method: To obtain the crop coefficient (Kc), the ratio between crop evapotranspiration (ETc), determined using the SLIMCAP system, and reference evapotranspiration (ET₀), estimated by the Penman-Monteith, Hargreaves-Samani, Solar Radiation, Blaney-Criddle, and Priestley-Taylor methods, was calculated. Results and Discussion: The accumulated ETc of the chive crop in a protected environment was 178.12 mm over a 35-day cycle, corresponding to an average daily ETc of 4.95 mm. The maximum water consumption of the chive crop was 7.56 mm per day, and the Kc values for chives under protected environment conditions are: Phase I: 0.59; Phase II: 0.80; Phase III: 1.06 (according to the FAO Penman-Monteith standard). Research Implications: This research can help seedling producers understand how the crop coefficient and crop evapotranspiration work, thereby contributing to plant production projects in protected environments. Originality/Value: The research is relevant as it addresses a crop that is rarely studied or mentioned in the literature, providing data applicable to sustainable management in protected environments.

A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanisms

Ketosis-prone diabetes mellitus (KPD) is a subtype of type 2 diabetes, which presents much like type 1 diabetes, with dramatic hyperglycemia and ketoacidosis. Although KPD patients are initially insulin-dependent, after a few months of insulin treatment, roughly 70% undergo near-normoglycemia remission and can maintain blood glucose without insulin, as in early type 2 diabetes or prediabetes. Here, we propose that these phenomena can be explained by the existence of a fast, reversible glucotoxicity process, which may exist in all people but be more pronounced in those susceptible to KPD. We develop a simple mathematical model of the pathogenesis of KPD, which incorporates this assumption, and show that it reproduces the phenomenology of KPD, including variations in the ability for patients to achieve and sustain remission. These results suggest that a variation of our model may be able to quantitatively describe variations in the course of remission among individuals with KPD.

Long Term Survivors of Anaplastic Thyroid Cancer: A Genomic Predictive Model

Abstract Context Longer-term survival is possible for some patients with Anaplastic Thyroid Cancer (ATC). However, genomic factors associated with improved survival are poorly characterized. Objective To develop a mathematical model to predict mutation-based survival risk in ATC. Design Retrospective cohort study of 204 ATC samples from the cBioPortal database, divided into 80% training and 20% validation cohorts. Multivariate analysis identified prognostic genes, used to construct a point-based risk model. KEGG pathway enrichment and BRAF subanalyses were performed. Setting Multi-institutional, international genomic database. Patients or Other Participants Samples were included if sequencing and survival data were available (N=204). Intervention(s) Not applicable Main Outcome Measure(s) The prespecified primary outcome was overall survival. Results Fourteen genes were associated with increased risk - TET1, MAPK12, ATP10A, PIK3CA, MUC4, PNPLA2, PLD4, EGLN2, BSN, FLNC, RADIL, ZMYND8, FRAS1, RECQL4. More aggressive (n=37) and less aggressive cohorts (n=128) were determined using the maximally selected rank statistic, yielding a point threshold of 0.27. The predictive performance of the risk model demonstrated a C-index of 0.74. On Kaplan Meier analysis, 1-year survival differed for more aggressive patients (0%) compared to less aggressive patients (32%). For the validation cohort, survival remained significantly different between risk cohorts and on BRAF subanalysis. Each risk cohort subsequently underwent KEGG pathway enrichment analysis which showed significantly increased enrichment across several pathways for more aggressive tumors. Conclusions This model identifies mutated genes that are associated with the most aggressive ATCs and thus may aid in preoperative risk assessment when evaluating patients for surgery for curative intent.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ МЕТОДОВ ЭЛЕКТРИЧЕСКОГО ЗОНДИРОВАНИЯ НА ОСНОВЕ ЭЛЕКТРОСТАТИЧЕСКОЙ АНАЛОГИИ И МЕТОДА ТЕОРЕМ СЛОЖЕНИЯ

A mathematical model of electrical sounding methods is proposed, which may include electrical structurography and electrical profiling. A generalized model of sounding methods is presented based on electrostatic analogy. A problem of mathematical physics is set for calculating the electric field potential in this model. The solution to the problem is obtained by the method of addition theorems and diagnostic equations are derived. By numerically solving these equations, the parameters of the heterogeneity can be determined, the detection of which is the purpose of sounding. The method for solving the problem is quite universal and can be extended to more complex cases

Mechanical Design in Tube Feet.

Hydrostatic skeletons enable the transmission of mechanical work through a soft body. Despite the ubiquity of these structures among animals, we have a relatively rudimentary understanding of how they operate mechanically. Here we consider a mathematical model of the mechanics of a relatively tractable hydrostatic skeleton, the tube feet of sea stars. Tube feet drive locomotion by generating a pushing force against the environment. This pushing force is created by transmission of pressure from one chamber, the ampulla, to another, the stem, which extends from the oral surface of the body. This system operates as a compound machine with a mechanical advantage (MA, the ratio of output to input force) that varies with the geometry of its two chambers. We present an analytical approach for parameterizing the model from morphometric measurements and predictions for representative morphologies. Our analysis predicts that MA initially increases as the stem extends, but collapses to zero near maximum extension. The decrease in force output occurs because the angle of cross-helical fiber winding in the stem approaches the critical point of 54.7○, an angle at which the force components exactly balance the hoop and longitudinal forces from pressure. Though producing no axial force at full extension, a bent tube foot can still generate perpendicular forces that generate torque to lift and propel the body as the degree of bend changes, a proposition that is supported by kinematic observations of the tube feet. These results provide a framework for understanding tube foot mechanics across echinoderms and highlight the functional significance of helical fiber arrangements in hydrostatic skeletons.

Age-targeted vaccination for reducing Clostridioides difficile infection in England: a coupled mathematical-economic modelling analysis.

Clostridioides difficile infection (CDI) is associated with high morbidity and mortality, emphasising the need for prophylaxis. The lead vaccine candidate recently demonstrated promising reductions in medically attended cases. Key risk factors for CDI were incorporated into a hospital-level mathematical model used to simulate the impact of the vaccine on reducing disease burden in England. Model outputs of interest included medically attended cases, intensive care admissions and deaths associated with CDI, as well as costs and quality-adjusted life years (QALYs). Hospital costs and costs of years of life lost due to premature mortality averted per vaccine course were computed for a 10-year time horizon. The epidemiological model demonstrated considerable benefits to targeting older age groups whereby vaccinating only those over the age of 74 years old (i.e. 9% of England's population) more than halved CDI cases and intensive care unit (ICU) admissions. Simulations also showed that this could be expected to reduce deaths by almost two-thirds and that around 20% of lives saved would be achieved through indirect benefits, i.e. due to reduced transmission to unvaccinated as well as vaccinated individuals. Issuing around 5 million vaccine courses in both the first and second year to protect the eldest, and 0.4 million annual courses thereafter to maintain effective coverage of all those over 64 years old, can be expected to avert £378 in costs (2023£) and gain 0.046 QALYs per vaccine course by the fourth year of rollout. Should a safe and efficacious C. difficile vaccine be licensed, it could be positioned very well for providing considerable economical and health benefits. This work guides how these gains could be maximised for England's population.

Materials‐Algorithm Co‐Optimization for Specific and Quantitative Gas Detection

ABSTRACTRapid, reliable, and quantitative formaldehyde detection has become increasingly important in the processing industry and environmental protection. As an intelligent electronic instrument, the realization of electronic noses (e‐noses) for quantitative gas detection relies on enhanced specificity. Here, we propose a materials‐algorithm co‐optimization (MACO) method that enables quantitative detection of formaldehyde in e‐nose. This approach employs thermokinetic feature engineering to optimize data quality and algorithm selection, thereby reducing dependence on data scale and computing power resources. Specific thermokinetic activation patterns for formaldehyde can be generated through a single materials processing strategy. Through a combination of thermokinetic feature‐driven machine learning, we demonstrated an e‐nose—comprising only five Co3O4‐based gas sensors—capable of discriminating formaldehyde from ethanol. The mathematical model reveals that the physicochemical mechanism of odor coding logic in our e‐nose is dictated by the mass action law. A quantitative detection of formaldehyde in 0.1–20 ppm with a precision of 5% full‐scale. has been demonstrated. We also showcase the adaptability of e‐nose for binary mixture analysis. The detection model of the MACO‐driven e‐nose is simple and interpretable, showing broad prospects to achieve quantitative gas detection rapidly and at a low cost.

Determining the moisture diffusion coefficient during soaking and cooking of chickpeas

This study aimed to apply a numerical/experimental approach to determine the moisture diffusion coefficient in chickpeas during the soaking and cooking processes, considering the seed swelling. The mathematical model combines Fick's second law to describe moisture transfer with the Peleg model to describe the expansion of the seed. It was solved numerically using finite differences method and fitted to experimental data of hydration kinetics at different temperature conditions (26, 40, 50, 63, 74, and 86 ºC). The numerical results showed that the D-values estimated considering deformable seeds were around 25-30 % greater than those estimated considering non-deformable seeds. This modeling approach could be useful in analyzing legumes' soaking and cooking process, but further studies are necessary to confirm its efficacy in different seed types and experimental conditions.

Multilayer networks describing urban interactions for building the digital twins of five cities in Spain

Abstract Networks specifying who interacts with whom are crucial for mathematical models of epidemic spreading. In the context of emerging diseases, these networks have the potential to encode multiple interaction contexts where non-pharmaceutical interventions can be introduced, allowing for proper comparisons among different intervention strategies in a plethora of contexts. Consequently, a multilayer network describing interactions in a population and detailing their contexts in different layers constitutes an appropriate tool for such descriptions. These approaches however become challenging in large-scale systems such as cities, particularly in a framework where data protection policies are enhanced. In this work, we present a methodology to build such multilayer networks and make those corresponding to five Spanish cities available. Our work uses approaches informed by multiple available datasets to create realistic digital twins of the citizens and their interactions and provides a playground to explore different pandemic scenario in realistic settings for better preparedness.

Performance Degradation in Monopulse Angle Measurement of Planar Phased-Array Due to Cross-Polarization Component

Due to the high-precision angle measurement performance, the monopulse technique plays a key role in fields such as remote sensing and space surveillance. The accuracy of monopulse angle measurement depends on the received amplitude and phase information, which is sensitive to the polarization component. Previous research has demonstrated that the performance of monopulse radar equipped with a parabolic antenna suffers from the cross-polarization component. However, it is not clear whether phased arrays (PAs) with higher degrees of freedom will also be affected by the cross-polarization component, and the parameter tolerance for performance degradation remains uncertain. In this paper, we establish a mathematical model of monopulse angle measurement in PA radar, which provides a comprehensive consideration of the cross-polarization component. Then, the received amplitude and phase patterns of PA radar are analyzed, and the theoretical angle errors caused by the cross-polarization jamming are derived. The experiments are conducted based on the measured amplitude-phase patterns of both co-polarization and cross-polarization. Experimental results are consistent with the theoretical analysis: the angle errors caused by cross-polarization jamming can reach half of the beamwidth in both azimuth and elevation dimensions, provided that the power of the cross-polarization and co-polarization components at the receiver is equal.

Impact and Cost-effectiveness of Regular Self-digital Anorectal Examination on Syphilis Among Gay, Bisexual, and Other Men Who Have Sex With Men: A Mathematical Modeling Study.

Rising syphilis incidence among Australian gay, bisexual, and other men who have sex with men (GBMSM) requires new early detection strategies. Regular self-digital anorectal examination (self-DARE) may facilitate syphilis identification, potentially reducing transmission. We evaluated its population-level impact and cost-effectiveness in controlling syphilis among Australian GBMSM. We developed an integrated transmission-dynamic and health-economic model, calibrated with 2012-2022 Australian GBMSM data. Over a 10-year period (2025-2034), we compared the base case with two scenarios: recommending self-DARE to men with higher sexual activity ("only high group") or to all individuals ("both groups"). We assessed changes in incidence, incremental cost-effectiveness ratios (ICERs), and benefit-cost ratios. The base case projected 110 501 new infections over 10 years. The "only high group" strategy averted 57 115 infections (51.7%) and was cost saving (negative ICER), with a benefit-cost ratio of 2.5. The "both groups" strategy averted more infections (58 216; 52.7%) but was less economically efficient (benefit-cost ratio: 1.6), though also cost-saving. Sensitivity analyses indicated that improving self-DARE sensitivity enhanced its performance. Self-DARE could effectively and cost-effectively reduce syphilis among GBMSM, particularly when focused on men with higher sexual activity. Further empirical research is needed to confirm its feasibility and effectiveness.

An Age-Structured Diffusive Model for Epidemic Modelling: Lie Symmetries and Exact Solutions

Abstract A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for similar purposes. The Lie symmetry classification of the model is derived. It is shown that the model admits an infinite-dimensional Lie algebra of invariance. Using the Lie symmetries, exact solutions, in particular those of the travelling wave types and in terms of special functions, are constructed. Examples of application of exact solutions with the correctly-specified parameters for calculation of the total number of infected individuals during an epidemic are presented.

Exploring optimal feedback delays of lane-keeping controller

This paper introduces a lane-keeping controller of vehicles considering two different time delays in the control loop. It focuses on the impact of time delays on system stability and control performance. A mathematical model for lane-keeping is used to design the hierarchical controller. The upper-level controller employs linear state feedback to determine the desired steering angle, considering different time delays corresponding to the lateral position and the yaw angle signals. The lower-level controller applies the steering torque via PD control to achieve the desired steering angle. The D-subdivision is utilised to analyse the linear stability of the rectilinear motion. The semi-discretization method is applied to provide the most stable control gains for various time delay combinations. It is shown that an appropriately increased time delay may not only expand the stable domain for the control gains, but it can also enhance the performance of the vehicle controller. The effectiveness and feasibility of the optimised hierarchical lane-keeping controller are verified through small-scale experiments.

Modeling the Temperature Dependence of Magneto-Optical Absorption Coefficients in Nanostructured Semiconductors

The article applies the temperature dependence of magneto-optical absorption coefficients in straight-zone nanostructured semiconductors. Two-dimensional combined state density 𝛼𝐵 2𝑑 (𝑁𝑆2𝑑 (𝐵), 𝑇) oscillations were used to calculate the temperature dependence of magneto-optical absorption coefficient oscillations. A mathematical model for determining 𝛼𝐵2𝑑 (𝑁𝑆2𝑑 (𝐵), 𝑇) has been developed for quantum-sized straight-zone semiconductor materials.

Statistical analysis supports the size control mechanism of Chlamydia development.

Chlamydia is an intracellular bacterium that reproduces via an unusual developmental cycle that only occurs within a eukaryotic host cell. A replicating form of the bacterium (RB) repeatedly divides to produce about a thousand progeny, which convert in a delayed and asynchronous manner into the infectious form (EB). The regulatory mechanisms that control this developmental switch are unknown, but they could potentially include extrinsic signals from the host cell or other chlamydiae, or an intrinsic signal such as chlamydial cell size. In this paper, we investigated the regulation of RB-to-EB conversion by developing and analyzing three mathematical models, each based on a different regulatory mechanism. To test these models, we derived statistical evidence from parameters, including number, size and location of RBs and EBs, obtained from experimental measurements and model fitting. All three models successfully reproduced the experimentally measured timing of RB-to-EB conversion and growth curves of the developmental forms in an infected cell. However, only the size control model, which postulates that RB size is an intrinsic signal that regulates the timing of RB-to-EB conversion, reproduced two additional statistical properties of the intracellular infection. These properties are a positive correlation between the number of RBs and EBs throughout the developmental cycle and the monotonic evolution of the coefficient of variation of EB number. This analysis thus provides support for the size control model.

Assessing the Impact of Migration on Corruption Dynamics

ABSTRACTHuman movement of population plays an important role in the geographical spread of corruption at different levels of predominance. In this work, we have proposed a two‐patch mathematical model in order to examine the effect of human movement on corruption dynamics with different levels of prevalence between patches. Using the next‐generation matrix technique, the basic reproduction number at corruption‐free equilibrium was computed. Analysis of the model reveals that it has exactly four equilibriums, namely, corruption‐free equilibrium, two boundary endemic equilibria, and endemic equilibrium. The stability analysis results indicate that when the , the corruption‐free equilibrium points are asymptotically stable both locally and globally, whereas the endemic equilibrium points are asymptotically stable locally when the . In addition, the model's parameter sensitivity was examined. Numerical simulations indicate that people migration can help the corruption to become endemic in both patches, even though the corruption can die out in each isolated patch. However, if movement rates are continuously increased, the corruption may endemic again in both patches.

Epigenetic age and fertility timeline: testing an epigenetic clock to forecast in vitro fertilization success rate.

In the field of in vitro fertilization (IVF), the search for reliable success predictors is ongoing, with novel biomarkers gaining increasing attention. Epigenetic clocks, mathematical models based on DNA methylation (DNAm) patterns, have revolutionized aging research by providing insights into biological aging. However, the magnitude of the benefit of the use of a simplified and non-specific epigenetic clock is still insufficient to claim for its clinical use. We investigated the potential role of epigenetic clocks in predicting IVF success. This prospective observational study involved 379 women of reproductive age who underwent IVF treatment. On the day of recruitment, blood samples were collected, and genomic DNA was isolated from white blood cells. Epigenetic age was calculated using an algorithm based on the methylation patterns of 5 specific CpG sites and derived by pyrosequencing technique ("Zbieć-Piekarska2" model). Epigenetic age acceleration (EPA) was estimated from the residuals of a linear model, with epigenetic age regressed on chronological age. We compared the resulting epigenetic age and EPA between women who achieved a live birth and those who did not, alongside traditional ovarian reserve parameters (antral follicular count AFC; anti-müllerian hormone AMH). Among 379 women, 204 (54%) achieved LB. They were younger, had better ovarian reserve markers, retrieved more oocytes and had lower epigenetic age (36 ± 5 vs. 39 ± 5 years, p < 0.001) with moderate predictive power (area under the curve AUC = 0.652). After adjusting for antral follicular count (AFC), epigenetic age remained significantly associated with live birth (adjusted odds ratio OR = 0.91 per year; p < 0.001), suggesting IVF success is more likely in epigenetically younger women, beyond their ovarian reserve. This association was lost in subgroup analysis by infertility cause. In women aged 31-35, epigenetic age and EPA were the best predictors (AUC = 0.637). Combining epigenetic age with ovarian reserve markers slightly improved predictive accuracy (AUC = 0.692 with AFC, 0.693 with AMH) over chronological age alone (AUC = 0.672). Epigenetic clocks may enhance IVF success prediction, particularly in women between 31 and 35. Our findings support the need for further research in this area and emphasize the importance of developing epigenetic models specifically tailored to fertility outcomes.