Mathematical Biosciences and Engineering最新文献

The hippocampus is a small, yet intricate seahorse-shaped tiny structure located deep within the brain's medial temporal lobe. It is a crucial component of the limbic system, which is responsible for regulating emotions, memory, and spatial navigation. This research focuses on automatic hippocampus segmentation from Magnetic Resonance (MR) images of a human head with high accuracy and fewer false positive and false negative rates. This segmentation technique is significantly faster than the manual segmentation methods used in clinics. Unlike the existing approaches such as UNet and Convolutional Neural Networks (CNN), the proposed algorithm generates an image that is similar to a real image by learning the distribution much more quickly by the semi-supervised iterative learning algorithm of the Deep Neuro-Fuzzy (DNF) technique. To assess its effectiveness, the proposed segmentation technique was evaluated on a large dataset of 18,900 images from Kaggle, and the results were compared with those of existing methods. Based on the analysis of results reported in the experimental section, the proposed scheme in the Semi-Supervised Deep Neuro-Fuzzy Iterative Learning System (SS-DNFIL) achieved a 0.97 Dice coefficient, a 0.93 Jaccard coefficient, a 0.95 sensitivity (true positive rate), a 0.97 specificity (true negative rate), a false positive value of 0.09 and a 0.08 false negative value when compared to existing approaches. Thus, the proposed segmentation techniques outperform the existing techniques and produce the desired result so that an accurate diagnosis is made at the earliest stage to save human lives and to increase their life span.

In this article, we reconsider the classical target cell limited dynamical within-host HIV model, solely taking into account the interaction between $ {rm{CD}}4^{+} $ T cells and virus particles. First, we summarize some analytical results regarding the corresponding dynamical system. For that purpose, we proved some analytical results regarding the system of differential equations as our first main contribution. Specifically, we showed non-negativity and boundedness of solutions, global existence in time and global uniqueness in time and examined stability properties of two possible equilibria. In particular, we demonstrated that the virus-free equilibrium and the plateau-phase equilibrium are locally asymptotically stable using the Routh-Hurwitz criterion under appropriate conditions. As our second main contribution, we underline our theoretical findings through some numerical experiments with standard Runge-Kutta time stepping schemes. We conclude this work with a summary of our main results and a suggestion of an extension for more complex dynamical systems with regard to HIV-infection.

Environmental changes are a growing concern, as they exert pressures on ecosystems. In some cases, such changes lead to shifts in ecosystem structure. However, species can adapt to changes through evolution, and it is unclear how evolution interacts with regime shifts, which restricts ecosystem management strategies. Here, we used a model of prey population with evolution and intra-specific trait diversity, and simulated regime shifts through changes in predation pressure. We then explored interactions between evolution, diversity, and shifts in population density. Evolution induced delayed or early regime shifts, and altered the recovery of populations. Such changes depended on the relative speed of evolution and change of predation pressure, as well as on the initial state of the population. Evolution also influenced population resilience, which was important when considering strong environmental variability. For instance, storms can spontaneously increase mortality and induce shifts. Furthermore, environmental variability induced even higher mortality if the phenotypic diversity of populations is large. Some phenotypes were more vulnerable to environmental changes, and such increases in mortality favor shifts to decreases in density. Thus, population management needs to consider diversity, evolution, and environmental change altogether to better anticipate regime shifts on eco-evolutionary time scales. Here, evolution and diversity showed complex interactions with population shift dynamics. Investigating the influence of higher diversity levels, such as diversity at a community level, should be another step towards anticipating changes in ecosystems and communities.

We present a modeling strategy to forecast the incidence rate of dengue in the department of Córdoba, Colombia, thereby considering the effect of climate variables. A Seasonal Autoregressive Integrated Moving Average model with exogenous variables (SARIMAX) model is fitted under a cross-validation approach, and we examine the effect of the exogenous variables on the performance of the model. This study uses data of dengue cases, precipitation, and relative humidity reported from years 2007 to 2021. We consider three configurations of sizes training set-test set: 182-13,189-6, and 192-3. The results support the theory of the relationship between precipitation, relative humidity, and dengue incidence rate. We find that the performance of the models improves when the time series models are previously adjusted for each of the exogenous variables, and their forecasts are used to determine the future values of the dengue incidence rate. Additionally, we find that the configurations 189-6 and 192-3 present the most consistent results with regard to the model's performance in the training and test data sets.

In this paper, we introduce and analyze a discrete-time model of an epidemic spread in a heterogeneous population. As the heterogeneous population, we define a population in which we have two groups which differ in a risk of getting infected: a low-risk group and a high-risk group. We construct our model without discretization of its continuous-time counterpart, which is not a common approach. We indicate functions that reflect the probability of remaining healthy, which are based on the mass action law. Additionally, we discuss the existence and local stability of the stability states that appear in the system. Moreover, we provide conditions for their global stability. Some of the results are expressed with the use of the basic reproduction number $ mathcal{R}_0 $. The novelty of our paper lies in assuming different values of every coefficient that describe a given process in each subpopulation. Thanks to that, we obtain the pure population's heterogeneity. Our results are in a line with expectations - the disease free stationary state is locally stable for $ mathcal{R}_0 < 1 $ and loses its stability after crossing $ mathcal{R}_0 = 1 $. We supplement our results with a numerical simulation that concerns the real case of a tuberculosis epidemic in Poland.

In the pursuit of personalized medicine, there is a growing demand for computational models with parameters that are easily obtainable to accelerate the development of potential solutions. Blood tests, owing to their affordability, accessibility, and routine use in healthcare, offer valuable biomarkers for assessing hemostatic balance in thrombotic and bleeding disorders. Incorporating these biomarkers into computational models of blood coagulation is crucial for creating patient-specific models, which allow for the analysis of the influence of these biomarkers on clot formation. This systematic review aims to examine how clinically relevant biomarkers are integrated into computational models of blood clot formation, thereby advancing discussions on integration methodologies, identifying current gaps, and recommending future research directions. A systematic review was conducted following the PRISMA protocol, focusing on ten clinically significant biomarkers associated with hemostatic disorders: D-dimer, fibrinogen, Von Willebrand factor, factor Ⅷ, P-selectin, prothrombin time (PT), activated partial thromboplastin time (APTT), antithrombin Ⅲ, protein C, and protein S. By utilizing this set of biomarkers, this review underscores their integration into computational models and emphasizes their integration in the context of venous thromboembolism and hemophilia. Eligibility criteria included mathematical models of thrombin generation, blood clotting, or fibrin formation under flow, incorporating at least one of these biomarkers. A total of 53 articles were included in this review. Results indicate that commonly used biomarkers such as D-dimer, PT, and APTT are rarely and superficially integrated into computational blood coagulation models. Additionally, the kinetic parameters governing the dynamics of blood clot formation demonstrated significant variability across studies, with discrepancies of up to 1, 000-fold. This review highlights a critical gap in the availability of computational models based on phenomenological or first-principles approaches that effectively incorporate affordable and routinely used clinical test results for predicting blood coagulation. This hinders the development of practical tools for clinical application, as current mathematical models often fail to consider precise, patient-specific values. This limitation is especially pronounced in patients with conditions such as hemophilia, protein C and S deficiencies, or antithrombin deficiency. Addressing these challenges by developing patient-specific models that account for kinetic variability is crucial for advancing personalized medicine in the field of hemostasis.

As an essential component of mechanical systems, bearing fault diagnosis is crucial to ensure the safe operation of the equipment. However, vibration data from bearings often exhibit non-stationary and nonlinear features, which complicates fault diagnosis. To address this challenge, this paper introduces a novel multi-scale time-frequency and statistical features fusion model (MTSF-FM). Specifically, the method first employs continuous wavelet transform to generate time-frequency images, capturing local and global features of the signal at different scales. Contrast enhancement techniques are then used to improve the visual quality of these images. Next, features are extracted from the time-frequency images using a visual geometry group network to obtain deep features of image modalities. In parallel, 13 key features are extracted from the original vibration data in the time-frequency domain. Convolutional neural networks are then employed for deep feature extraction. Experimental results demonstrate that MTSF-FM achieves accuracies of 98.5% and 95.1% on two public datasets. These findings highlight the effectiveness of MTSF-FM in analyzing complex vibration data and propose a novel method for bearing fault diagnosis.

Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the "no control" scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the "reconstructed" scenario, representing real-world data and interventions, (ⅲ) the "social distancing control" scenario covering a broad set of behavioral changes, (ⅳ) the "vaccine control" scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the "both controls concurrently" scenario incorporating social distancing and vaccine controls simultaneously. By comparing these scenarios, we provided a comprehensive analysis of various intervention strategies, offering valuable insights into disease dynamics. Our innovative approach to modeling the cost of control gave rise to a robust computational algorithm for solving optimal control problems associated with different public health regulations. Numerical results were supported by real data for the Delta variant of the COVID-19 pandemic in the United States.