Mathematical Biosciences and Engineering最新文献

Ant colonies demonstrate a finely tuned alarm response to potential threats, offering a uniquely manageable empirical setting for exploring adaptive information diffusion within groups. To effectively address potential dangers, a social group must swiftly communicate the threat throughout the collective while conserving energy in the event that the threat is unfounded. Through a combination of modeling, simulation, and empirical observations of alarm spread and damping patterns, we identified the behavioral rules governing this adaptive response. Experimental trials involving alarmed ant workers (Pogonomyrmex californicus) released into a tranquil group of nestmates revealed a consistent pattern of rapid alarm propagation followed by a comparatively extended decay period [1]. The experiments in [1] showed that individual ants exhibiting alarm behavior increased their movement speed, with variations in response to alarm stimuli, particularly during the peak of the reaction. We used the data in [1] to investigate whether these observed characteristics alone could account for the swift mobility increase and gradual decay of alarm excitement. Our self-propelled particle model incorporated a switch-like mechanism for ants' response to alarm signals and individual variations in the intensity of speed increased after encountering these signals. This study aligned with the established hypothesis that individual ants possess cognitive abilities to process and disseminate information, contributing to collective cognition within the colony (see [2] and the references therein). The elements examined in this research support this hypothesis by reproducing statistical features of the empirical speed distribution across various parameter values.

Early diagnosis of abnormal electrocardiogram (ECG) signals can provide useful information for the prevention and detection of arrhythmia diseases. Due to the similarities in Normal beat (N) and Supraventricular Premature Beat (S) categories and imbalance of ECG categories, arrhythmia classification cannot achieve satisfactory classification results under the inter-patient assessment paradigm. In this paper, a multi-path parallel deep convolutional neural network was proposed for arrhythmia classification. Furthermore, a global average RR interval was introduced to address the issue of similarities between N vs. S categories, and a weighted loss function was developed to solve the imbalance problem using the dynamically adjusted weights based on the proportion of each class in the input batch. The MIT-BIH arrhythmia dataset was used to validate the classification performances of the proposed method. Experimental results under the intra-patient evaluation paradigm and inter-patient evaluation paradigm showed that the proposed method could achieve better classification results than other methods. Among them, the accuracy, average sensitivity, average precision, and average specificity under the intra-patient paradigm were 98.73%, 94.89%, 89.38%, and 98.24%, respectively. The accuracy, average sensitivity, average precision, and average specificity under the inter-patient paradigm were 91.22%, 89.91%, 68.23%, and 95.23%, respectively.

The dynamic behavior of a discrete-time two-patch model with the Allee effect and nonlinear dispersal is studied in this paper. The model consists of two patches connected by the dispersal of individuals. Each patch has its own carrying capacity and intraspecific competition, and the growth rate of one patch exhibits the Allee effect. The existence and stability of the fixed points for the model are explored. Then, utilizing the central manifold theorem and bifurcation theory, fold and flip bifurcations are investigated. Finally, numerical simulations are conducted to explore how the Allee effect and nonlinear dispersal affect the dynamics of the system.

This paper is concerned with invariant measures of fractional stochastic delay Ginzburg-Landau equations on the entire space $ mathbb{R}^n $. We first derive the uniform estimates and the mean-square uniform smallness of the tails of solutions in corresponding space. Then we deduce the weak compactness of a set of probability distributions of the solutions applying the Ascoli-Arzel$ grave{a} $. We finally prove the existence of invariant measures by applying Krylov-Bogolyubov's method.

We study an extension of the stochastic SIS (Susceptible-Infectious-Susceptible) model in continuous time that accounts for variation amongst individuals. By examining its limiting behaviour as the population size grows we are able to exhibit conditions for the infection to become endemic.

A new network-based SIR epidemic model with saturated incidence rate and nonlinear recovery rate is proposed. We adopt an edge-compartmental approach to rewrite the system as a degree-edge-mixed model. The explicit formula of the basic reproduction number $ mathit{boldsymbol{R_{0}}} $ is obtained by renewal equation and Laplace transformation. We find that $ mathit{boldsymbol{R_{0}}} < 1 $ is not enough to ensure global asymptotic stability of the disease-free equilibrium, and when $ mathit{boldsymbol{R_{0}}} > 1 $, the system can exist multiple endemic equilibria. When the number of hospital beds is small enough, the system will undergo backward bifurcation at $ mathit{boldsymbol{R_{0}}} = 1 $. Moreover, it is proved that the stability of feasible endemic equilibrium is determined by signs of tangent slopes of the epidemic curve. Finally, the theoretical results are verified by numerical simulations. This study suggests that maintaining sufficient hospital beds is crucial for the control of infectious diseases.

Knee medial compartment osteoarthritis is effectively treated by a medial open-wedge high tibial osteotomy (MOWHTO). The feasibility and safety of MOWHTO for mild lateral meniscal tears are unknown. This study examined the feasibility and safety of knee joint weight-bearing line ratio (WBLr) adjustment during MOWHTO with lateral meniscal injuries. We used a healthy adult male's lower extremities computed tomography scans and knee joint magnetic resonance imaging images to create a normal fine element (FE) model. Based on this model, we generated nine FE models for the MOWHTO operation (WBLr: 40-80%) and 15 models for various lateral meniscal injuries. A compressive load of 650N was applied to all cases to calculate the von Mises stress (VMS), and the intact lateral meniscus' maximal VMS at 77.5% WBLr was accepted as the corrective upper limit stress. Our experimental results show that mild lateral meniscal tears can withstand MOWHTO, while severe tears cannot. Our findings expand the use of MOWHTO and provide a theoretical direction for practical decisions in patients with lateral meniscal injuries.

Currently, with the rapid growth of online media, more people are obtaining information from it. However, traditional hotspot mining algorithms cannot achieve precise and fast control of hot topics. Aiming at the problem of poor accuracy and timeliness in current news media hotspot mining methods, this paper proposes a hotspot mining method based on the co-occurrence word model. First, a new co-occurrence word model based on word weight is proposed. Then, for key phrase extraction, a hotspot mining algorithm based on the co-occurrence word model and improved smooth inverse frequency rank (SIFRANK) is designed. Finally, the Spark computing framework is introduced to improve the computing efficiency. The experimental outcomes expresses that the new word discovery algorithm discovered 16871 and 17921 new words in the Weibo Short News and Weibo Short Text datasets respectively. The heat weight values of the keywords obtained by the improved SIFRANK reaches 0.9356, 0.9991, and 0.6117. In the Covid19 Tweets dataset, the accuracy is 0.6223, the recall is 0.7015, and the F1 value is 0.6605. In the President-elects Tweets dataset, the accuracy is 0.6418, the recall is 0.7162, and the F1 value is 0.6767. After applying the Spark computing framework, the running speed has significantly improved. The text mining news media hotspot mining method based on the co-occurrence word model proposed in this study has improved the accuracy and efficiency of mining hot topics, and has great practical significance.

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

Trigeminal neuralgia is a debilitating condition characterized by severe facial pain. Carbamazepine has been widely used as a first-line treatment option for trigeminal neuralgia, but there is a need to evaluate its safety and efficacy based on existing evidence. This meta-analysis aims to systematically assess the available literature and provide a comprehensive evaluation of the safety and efficacy of carbamazepine in the treatment of trigeminal neuralgia. A thorough search of electronic databases yielded a total of 15 relevant studies that met the inclusion criteria. The pooled analysis of these studies revealed that carbamazepine demonstrated significant efficacy in reducing pain intensity and frequency in patients with trigeminal neuralgia. Moreover, the drug was generally well-tolerated, with the most common adverse events being mild and transient. Subgroup analyses based on different dosages and treatment durations further supported the overall findings. However, caution should be exercised in patients with certain comorbidities or specific populations, as some rare but severe adverse events were reported. In conclusion, this meta-analysis provides strong evidence supporting the safety and efficacy of carbamazepine as a valuable therapeutic option for the management of trigeminal neuralgia. These results can guide clinicians in making informed decisions regarding the use of carbamazepine and contribute to optimizing treatment strategies for patients with trigeminal neuralgia. Further research is warranted to explore long-term safety and efficacy outcomes, as well as to compare carbamazepine with alternative treatment modalities.