Archana N Timsina, Yuganthi R Liyanage, Maia Martcheva, Necibe Tuncer
{"title":"A novel within-host model of HIV and nutrition.","authors":"Archana N Timsina, Yuganthi R Liyanage, Maia Martcheva, Necibe Tuncer","doi":"10.3934/mbe.2024246","DOIUrl":"https://doi.org/10.3934/mbe.2024246","url":null,"abstract":"<p><p>In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ mathcal{R}_0 < 1 $, and unstable when $ mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5577-5603"},"PeriodicalIF":2.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dae Hyeon Kim, Jin-Oh Park, Dae-Young Lee, Young-Seok Choi
{"title":"Multiscale distribution entropy analysis of short epileptic EEG signals.","authors":"Dae Hyeon Kim, Jin-Oh Park, Dae-Young Lee, Young-Seok Choi","doi":"10.3934/mbe.2024245","DOIUrl":"https://doi.org/10.3934/mbe.2024245","url":null,"abstract":"<p><p>This paper proposes an information-theoretic measure for discriminating epileptic patterns in short-term electroencephalogram (EEG) recordings. Considering nonlinearity and nonstationarity in EEG signals, quantifying complexity has been preferred. To decipher abnormal epileptic EEGs, i.e., ictal and interictal EEGs, via short-term EEG recordings, a distribution entropy (DE) is used, motivated by its robustness on the signal length. In addition, to reflect the dynamic complexity inherent in EEGs, a multiscale entropy analysis is incorporated. Here, two multiscale distribution entropy (MDE) methods using the coarse-graining and moving-average procedures are presented. Using two popular epileptic EEG datasets, i.e., the Bonn and the Bern-Barcelona datasets, the performance of the proposed MDEs is verified. Experimental results show that the proposed MDEs are robust to the length of EEGs, thus reflecting complexity over multiple time scales. In addition, the proposed MDEs are consistent irrespective of the selection of short-term EEGs from the entire EEG recording. By evaluating the Man-Whitney U test and classification performance, the proposed MDEs can better discriminate epileptic EEGs than the existing methods. Moreover, the proposed MDE with the moving-average procedure performs marginally better than one with the coarse-graining. The experimental results suggest that the proposed MDEs are applicable to practical seizure detection applications.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5556-5576"},"PeriodicalIF":2.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael R Lin, Xiaohui Guo, Asma Azizi, Jennifer H Fewell, Fabio Milner
{"title":"Mechanistic modeling of alarm signaling in seed-harvester ants.","authors":"Michael R Lin, Xiaohui Guo, Asma Azizi, Jennifer H Fewell, Fabio Milner","doi":"10.3934/mbe.2024244","DOIUrl":"https://doi.org/10.3934/mbe.2024244","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5536-5555"},"PeriodicalIF":2.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Arrhythmia classification based on multi-feature multi-path parallel deep convolutional neural networks and improved focal loss.","authors":"Zhongnan Ran, Mingfeng Jiang, Yang Li, Zhefeng Wang, Yongquan Wu, Wei Ke, Ling Xia","doi":"10.3934/mbe.2024243","DOIUrl":"https://doi.org/10.3934/mbe.2024243","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5521-5535"},"PeriodicalIF":2.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal.","authors":"Minjuan Gao, Lijuan Chen, Fengde Chen","doi":"10.3934/mbe.2024242","DOIUrl":"https://doi.org/10.3934/mbe.2024242","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5499-5520"},"PeriodicalIF":2.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Studies on invariant measures of fractional stochastic delay Ginzburg-Landau equations on R<sup>n</sup>.","authors":"Hong Lu, Linlin Wang, Mingji Zhang","doi":"10.3934/mbe.2024241","DOIUrl":"https://doi.org/10.3934/mbe.2024241","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5456-5498"},"PeriodicalIF":2.6,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An SIS epidemic model with individual variation.","authors":"Philip K Pollett","doi":"10.3934/mbe.2024240","DOIUrl":"https://doi.org/10.3934/mbe.2024240","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5446-5455"},"PeriodicalIF":2.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach.","authors":"Fang Wang, Juping Zhang, Maoxing Liu","doi":"10.3934/mbe.2024239","DOIUrl":"https://doi.org/10.3934/mbe.2024239","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5430-5445"},"PeriodicalIF":2.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lin Chen, Mingjun Wang, Zhanyu Wu, Jinbo Sun, Jianglong Li, Chun Chen, Chuan Ye
{"title":"Advancements in health informatics: finite element insights into medial open-wedge high tibial osteotomy and lateral meniscal tears.","authors":"Lin Chen, Mingjun Wang, Zhanyu Wu, Jinbo Sun, Jianglong Li, Chun Chen, Chuan Ye","doi":"10.3934/mbe.2024237","DOIUrl":"https://doi.org/10.3934/mbe.2024237","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5394-5410"},"PeriodicalIF":2.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Co-occurrence word model for news media hotspot mining-text mining method design.","authors":"Xinyun Zhang, Tao Ding","doi":"10.3934/mbe.2024238","DOIUrl":"https://doi.org/10.3934/mbe.2024238","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5411-5429"},"PeriodicalIF":2.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141318767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}