Mathematical Biosciences and Engineering最新文献

In this work, we formulated a mathematical model to describe growth, acquisition of bacterial resistance, and immune response for Helicobacter pylori (H. pylori). The qualitative analysis revealed the existence of five equilibrium solutions: (ⅰ) An infection-free state, in which the bacterial population and immune cells are suppressed, (ⅱ) an endemic state only with resistant bacteria without immune cells, (ⅲ) an endemic state only with resistant bacteria and immune cells, (ⅳ) an endemic state of bacterial coexistence without immune cells, and (ⅴ) an endemic coexistence state with immune response. The stability analysis showed that the equilibrium solutions (ⅰ) and (ⅳ) are locally asymptotically stable, whereas the equilibria (ⅱ) and (ⅲ) are unstable. We found four threshold conditions that establish the existence and stability of equilibria, which determine when the populations of sensitive H. pylori and resistant H. pylori are controlled or eliminated, or when the infection progresses only with resistant bacteria or with both bacterial populations. The numerical simulations corroborated the qualitative analysis, and provided information on the emergence of a limit cycle that breaks the stability of the coexistence equilibrium. The results revealed that the key to controlling bacterial progression is to keep bacterial growth thresholds below 1; this can be achieved by applying an appropriate combination of antibiotics and correct stimulation of the immune response. Otherwise, when bacterial growth thresholds exceed 1, the bacterial persistence scenarios mentioned above occur.

Bone age assessment (BAA) is a widely used clinical practice for the biological development of adolescents. The Tanner Whitehouse (TW) method is a traditionally mainstream method that manually extracts multiple regions of interest (ROIs) related to skeletal maturity to infer bone age. In this paper, we propose a deep learning-based method for fully automatic ROIs localization and BAA. The method consists of two parts: a U-net-based backbone, selected for its strong performance in semantic segmentation, which enables precise and efficient localization without the need for complex pre- or post-processing. This method achieves a localization precision of 99.1% on the public RSNA dataset. Second, an InceptionResNetV2 network is utilized for feature extraction from both the ROIs and the whole image, as it effectively captures both local and global features, making it well-suited for bone age prediction. The BAA neural network combines the advantages of both ROIs-based methods (TW3 method) and global feature-based methods (GP method), providing high interpretability and accuracy. Numerical experiments demonstrate that the method achieves a mean absolute error (MAE) of 0.38 years for males and 0.45 years for females on the public RSNA dataset, and 0.41 years for males and 0.44 years for females on an in-house dataset, validating the accuracy of both localization and prediction.

Reaction-diffusion equations are a trusted modeling framework for the dynamics of biological populations in space and time, and their traveling wave solutions are interpreted as the density of an invasive species that spreads at constant speed. Even though certain species can significantly alter their abiotic environment for their benefit, and even though some of these so-called "ecosystem engineers" are among the most destructive invasive species, most models neglect this feedback. Here, we extended earlier work that studied traveling waves of ecosystem engineers with a logistic growth function to study the existence of traveling waves in the presence of a strong Allee effect. Our model consisted of suitable and unsuitable habitat, each a semi-infinite interval, separated by a moving interface. The speed of this boundary depended on the engineering activity of the species. On each of the intervals, we had a reaction-diffusion equation for the population density, and at the interface, we had matching conditions for density and flux. We used phase-plane analysis to detect and classify several qualitatively different types of traveling waves, most of which have previously not been described. We gave conditions for their existence for different biological scenarios of how individuals alter their abiotic environment. As an intermediate step, we studied the existence of traveling waves in a so-called "moving habitat model", which can be interpreted as a model for the effects of climate change on the spatial dynamics of populations.

It has been clearly demonstrated over the past years that control theory can provide an efficient framework for the solution of several complex tasks in epidemiology. In this paper, we present a computational approach for the state estimation based reference tracking control and historical data reconstruction using nonlinear compartmental epidemic models. The control model is given in nonlinear input-affine form, where the manipulable input is the disease transmission rate influenced by possible measures and restrictions, while the observed or computed output is the number of infected people. The control design is built around a simple SEIR model and relies on a feedback linearization technique. We examine and compare different control setups distinguished by the availability of state information, complementing the directly measurable data with an extended Kalman filter used for state estimation. To illustrate the capabilities and robustness of the proposed method, we carry out multiple case studies for output tracking and data reconstruction on Swedish and Hungarian data, all in the presence of serious model and parameter mismatch. Computation results show that a well-designed feedback, even in the presence of significant observation uncertainties, can sufficiently reduce the effect of modeling errors.

Forecasting wind speed plays an increasingly essential role in the wind energy industry. However, wind speed is uncertain with high changeability and dependency on weather conditions. Variability of wind energy is directly influenced by the fluctuation and unpredictability of wind speed. Traditional wind speed prediction methods provide deterministic forecasting that fails to estimate the uncertainties associated with wind speed predictions. Modeling those uncertainties is important to provide reliable information when the uncertainty level increases. Models for estimating prediction intervals of wind speed do not differentiate between daytime and nighttime shifts, which can affect the performance of probabilistic wind speed forecasting. In this paper, we introduce a prediction framework for deterministic and probabilistic short-term wind speed forecasting. The designed framework incorporates independent machine learning (ML) models to estimate point and interval prediction of wind speed during the daytime and nighttime shifts, respectively. First, feature selection techniques were applied to maintain the most relevant parameters in the datasets of daytime and nighttime shifts, respectively. Second, support vector regressors (SVRs) were used to predict the wind speed 10 minutes ahead. After that, we incorporated the non-parametric kernel density estimation (KDE) method to statistically synthesize the wind speed prediction errors and estimate the prediction intervals (PI) with several confidence levels. The simulation results validated the effectiveness of our framework and demonstrated that it can generate prediction intervals that are satisfactory in all evaluation criteria. This verifies the validity and feasibility of the hypothesis of separating the daytime and nighttime data sets for these types of predictions.

We considered three types of stochastic models of a single population growth: with diffusion-type noise; with parameters replaced by stochastic processes; and with random jumps describing a sudden decrease in population size. We presented methods for studying stochastic processes modeling population growth, in particular, the long-time behavior of sample paths and their distributions. We were especially interested in the asymptotic stability of the density of the distributions of these processes. We gave biological interpretations, examples, and numerical simulations of theoretical methods and results.

Epileptic seizures, a prevalent neurological condition, necessitate precise and prompt identification for optimal care. Nevertheless, the intricate characteristics of electroencephalography (EEG) signals, noise, and the want for real-time analysis require enhancement in the creation of dependable detection approaches. Despite advances in machine learning and deep learning, capturing the intricate spatial and temporal patterns in EEG data remains challenging. This study introduced a novel deep learning framework combining a convolutional neural network (CNN), bidirectional gated recurrent unit (BiGRU), and convolutional block attention module (CBAM). The CNN extracts spatial features, the BiGRU captures long-term temporal dependencies, and the CBAM emphasizes critical spatial and temporal regions, creating a hybrid architecture optimized for EEG pattern recognition. Evaluation of a public EEG dataset revealed superior performance compared to existing methods. The model achieved 99.00% accuracy in binary classification, 96.20% in three-class tasks, 92.00% in four-class scenarios, and 89.00% in five-class classification. High sensitivity (89.00-99.00%) and specificity (89.63-99.00%) across all tasks highlighted the model's robust ability to identify diverse EEG patterns. This approach supports healthcare professionals in diagnosing epileptic seizures accurately and promptly, improving patient outcomes and quality of life.

Recently, glioblastoma tumors were shown to form tumor microtubes, which are thin, long protrusions that help the tumor grow and spread. Follow-up experiments were conducted on mice in order to test what impact the tumor microtubes have on tumor regrowth after the partial removal of a tumor region. The surgery was performed in isolation and along with growth-inhibiting treatments such as a tumor microtube-inhibiting treatment and an anti-inflammatory treatment. Here, we have proposed a partial differential equation model applicable to describe the microtube-driven regrowth of the cancer in the lesion. We found that the model is able to replicate the main trends seen in the experiments such as fast regrowth, larger cancer density in the lesion, and further spread into healthy tissue. The model indicates that the dominant mechanisms of re-growth are growth-inducing wound-healing mechanisms and the proliferative advantage from the tumor microtubes. In addition, tumor microtubes provide orientational guidance from the untreated tissue into the lesion.