Mathematical Biosciences最新文献_第6页

A dynamic model for Waddington’s landscape accounting for cell-to-cell communication 沃丁顿景观的动态模型，用于解释细胞间的通信。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.mbs.2025.109537

Simon Merkt , Lara Fuhrmann , Erika Dudkin , Andreas Schlitzer , Barbara Niethammer , Jan Hasenauer

{"title":"A dynamic model for Waddington’s landscape accounting for cell-to-cell communication","authors":"Simon Merkt , Lara Fuhrmann , Erika Dudkin , Andreas Schlitzer , Barbara Niethammer , Jan Hasenauer","doi":"10.1016/j.mbs.2025.109537","DOIUrl":"10.1016/j.mbs.2025.109537","url":null,"abstract":"<div><div>Waddington’s landscape provides a conceptual model for developmental processes. It is the basis of various mathematical models describing cell maturation and development at cell and population levels. Yet, these mathematical models mostly disregard cell-to-cell communication, an essential process that modulates cellular decision-making and population dynamics.</div><div>In this study, we provide a dynamical model for cell maturation and development which can be seen as an extension of Waddington’s landscape. The coupled system of partial and ordinary differential equations describes cell density along the cell state together with ligand concentrations. Cell-state-dependent ligand production determines ligand availability, which controls population-level processes. We provide proof of the existence and uniqueness of solutions for our coupled differential equation system and demonstrate the model’s validity by analyzing single-cell transcriptomics data. Our results show that cell-to-cell communication is essential for accurately depicting biological recovery processes, such as the regeneration of stem cells in the intestine’s crypt and the response of immune cells upon LSP stimulation.</div><div>Our findings underscore the importance of incorporating cell-to-cell communication into mathematical models of biological development. By doing so, we unlock the potential for deeper insights into complex processes such as tissue regeneration and immune responses, offering new avenues for understanding and predicting the dynamics of biological recovery and cell activation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109537"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145115771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling covalently closed circular DNA dynamics in assessing chronic hepatitis B prognosis 评估慢性乙型肝炎预后的共价闭环DNA动力学建模。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-11-11 DOI: 10.1016/j.mbs.2025.109568

Qiulin Huang , Qiang Li , Zaitang Huang , Yuming Wang , Guangyu Huang , Kaifa Wang , Wendi Wang

{"title":"Modeling covalently closed circular DNA dynamics in assessing chronic hepatitis B prognosis","authors":"Qiulin Huang , Qiang Li , Zaitang Huang , Yuming Wang , Guangyu Huang , Kaifa Wang , Wendi Wang","doi":"10.1016/j.mbs.2025.109568","DOIUrl":"10.1016/j.mbs.2025.109568","url":null,"abstract":"<div><div>The persistence of covalently closed circular DNA (cccDNA) in the nuclei of HBV-infected hepatocytes plays a critical role in the pathogenesis of chronic hepatitis B (CHB), and hepatitis B surface antigen (HBsAg) levels can be considered a surrogate marker for cccDNA quantification. In this paper, a mathematical model is proposed to mimic cccDNA kinetics in infected hepatocytes, and the basic reproduction rate of cccDNA is obtained. It is found that the backward bifurcation occurs. Importantly, the model predictions match well the clinical data from 96 newly treated CHB patients, collected at the authors’ hospitals. Specifically, 18 patients (23.96 %) achieved HBsAg serologic negative conversion (SNC), excluding 5 patients with serologic relapse. Ten patients were predicted to be uncertain, including two clinically confirmed patients with SNC. Excluding the uncertain patients, our model gives a concordance rate of 93.75 % (15/16). Our results suggest that the baseline HBsAg, HBV DNA and hepatitis e surface antigen statuses are the major factors related to the accuracy of the model for the prediction of negative conversion. Therefore, our model is helpful to design effective clinical withdrawal indicators.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109568"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145515354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Data-driven modeling and prediction of microglial cell dynamics in the ischemic penumbra 缺血半暗区小胶质细胞动力学的数据驱动建模和预测。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-10 DOI: 10.1016/j.mbs.2025.109549

Sara Amato , Andrea Arnold

引用次数: 0

Impact of latent delay and environment infection on tuberculosis dynamics in a population 潜伏延迟和环境感染对人群结核病动态的影响。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-31 DOI: 10.1016/j.mbs.2025.109566

Hui Cao , Xianyi Zhao , Xingfu Zou

{"title":"Impact of latent delay and environment infection on tuberculosis dynamics in a population","authors":"Hui Cao , Xianyi Zhao , Xingfu Zou","doi":"10.1016/j.mbs.2025.109566","DOIUrl":"10.1016/j.mbs.2025.109566","url":null,"abstract":"<div><div>In this paper we explore the impact of latency delay and infection by Mycobacterium tuberculosis in the environment on the spread of tuberculosis in a population. We first derive a delay differential equation model with environmental indirect transmission. We address the well-posenedness and identify the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> of the model. We then discuss the equilibria and their stability in terms of the composite threshold parameter <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> which determine whether or not the tuberculosis will go extinct of persist in the popolaiton: the disease free equilibrium is globally stable if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></math></span>, and it becomes unstable if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span>. In the latter case, there exists a unique endemic equilibrium, which is locally asymptotically stable when <span><math><mi>τ</mi></math></span> is sufficiently small; furthermore, we obtain the conditions for the existence of Hopf bifurcation around the endemic equilibrium. The condition implies that the interplay of the latency delay and infection of Mycobacterium tuberculosis in the environment may contribute not only to the TB’s persistence but also the way it persists: either as an constant pattern (endemic equilibrium) or as a periodic pattern (oscillation around the endemic equilibrium). We also discuss the epidemiological implication of the mathematical results.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109566"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145433401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability and bifurcation analysis of a predator–prey system with feedback-controlled odour and wind-driven decay 具有反馈控制气味和风驱动衰变的捕食-食饵系统的稳定性和分岔分析。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-28 DOI: 10.1016/j.mbs.2025.109561

Dipam Das , Debasish Bhattacharjee , Subarna Roy , Pankaj Kumar Tiwari

{"title":"Stability and bifurcation analysis of a predator–prey system with feedback-controlled odour and wind-driven decay","authors":"Dipam Das , Debasish Bhattacharjee , Subarna Roy , Pankaj Kumar Tiwari","doi":"10.1016/j.mbs.2025.109561","DOIUrl":"10.1016/j.mbs.2025.109561","url":null,"abstract":"<div><div>Chemical communication is a fundamental component of predator–prey interactions, significantly influencing prey vigilance and predator hunting efficiency. Despite its ecological importance, prevailing mathematical models commonly treat odour as a static or externally imposed parameter, thereby overlooking its inherently dynamic nature and the reciprocal feedback between chemical cues and population dynamics. In this study, we present a novel three-dimensional model incorporating odour concentration as a dynamic variable, directly influenced by predator density and species interactions. Our model captures odour production, its natural decay through environmental processes such as wind-mediated dissipation, and the resultant non-consumptive effects on prey, including stress-induced reductions and alterations in vigilance behaviour. We rigorously analyse the qualitative dynamics of the model. Specifically, we perform stability analyses of all biologically feasible equilibria and detect various bifurcation phenomena, such as transcritical and Hopf bifurcations. The dynamics of the system are also examined across various two-parametric spaces. Extensive numerical simulations corroborate our theoretical findings and facilitate a detailed investigation of parameter influences. Furthermore, we compute the normalized forward sensitivity index to quantify the relative impact of model parameters.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109561"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145410995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mechanistic embedding of concise physiological absorption models for enhanced prediction in population pharmacokinetic modeling of oral ibuprofen 简明生理吸收模型的机制嵌入增强口服布洛芬人群药代动力学模型预测。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-04 DOI: 10.1016/j.mbs.2025.109546

Enwei Bu , Xiaotian Wu , Jun Li , Jiangning Hu , Jianhong Wu

{"title":"Mechanistic embedding of concise physiological absorption models for enhanced prediction in population pharmacokinetic modeling of oral ibuprofen","authors":"Enwei Bu , Xiaotian Wu , Jun Li , Jiangning Hu , Jianhong Wu","doi":"10.1016/j.mbs.2025.109546","DOIUrl":"10.1016/j.mbs.2025.109546","url":null,"abstract":"<div><div>Ibuprofen, a commonly used non-steroidal anti-inflammatory drug (NSAID), exhibits considerable variability in pharmacokinetics following oral administration, particularly during the absorption phase. This study aimed to enhance the mechanistic understanding of ibuprofen absorption by developing and integrating physiologically-informed models of absorption within a population pharmacokinetic (PopPK) framework. Using existing datasets of ibuprofen plasma concentrations, two one-compartment PopPK models with linear elimination were developed: the Sequential Absorption Pharmacokinetic (SAPK) model, which accounts for pH-dependent gastrointestinal absorption, and the Partial Absorption Pharmacokinetic (PAPK) model, which reflects absorption triggered by gastric emptying. Both models adequately described the observed concentration–time profiles and explained individual variability in absorption. These findings offer valuable insight into ibuprofen absorption kinetics and support the advancement of personalized dosing strategies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109546"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145240710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analyzing the impact of threshold strategies on cancer treatment using non-smooth models 用非光滑模型分析阈值策略对癌症治疗的影响

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-10 DOI: 10.1016/j.mbs.2025.109559

Xingxiao Wu , Wenjie Qin , Sanyi Tang

{"title":"Analyzing the impact of threshold strategies on cancer treatment using non-smooth models","authors":"Xingxiao Wu , Wenjie Qin , Sanyi Tang","doi":"10.1016/j.mbs.2025.109559","DOIUrl":"10.1016/j.mbs.2025.109559","url":null,"abstract":"<div><div>Surgical immunotherapy combined treatment is considered a promising cancer treatment approach, but determining the optimal timing and intensity of treatment remains a significant challenge. To address this issue, this paper proposes and investigates two non-smooth tumor-immune models with dynamic threshold strategies. We first establish a state-dependent impulsive model to describe a single immunotherapy strategy. By analyzing the properties of the Poincaré map, we studied the existence and stability of order-k periodic solutions, proved the existence of chaotic behavior using the maximum Lyapunov exponent, and examined the effects of treatment intervals and the number of treatments under different initial conditions on treatment outcomes. Secondly, we establish and analyze a Filippov tumor-immune model with dual dynamic thresholds. We examine the existence of sliding modes and pseudo-equilibria, prove the existence and stability of three order-k periodic solutions, and further explore the emergence of chaotic phenomena through numerical simulations. Finally, based on the real data of the lung cancer patient, parameter estimation was performed using the least squares method, and the treatment effects of the patient under four different treatment strategies were predicted. The results show that compared to a single-threshold strategy, the dual-threshold strategy not only more effectively controls tumor cell density but also ensures that effector cells remain at a safe level.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109559"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bifurcation thresholds in a bi-trophic turbidostat system: Refuge-mediated critical transitions and delay-induced oscillatory regimes 双营养浊化器系统的分岔阈值：避难所介导的关键转变和延迟诱导的振荡制度。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-11 DOI: 10.1016/j.mbs.2025.109560

Yu Mu , Wing-Cheong Lo

{"title":"Bifurcation thresholds in a bi-trophic turbidostat system: Refuge-mediated critical transitions and delay-induced oscillatory regimes","authors":"Yu Mu , Wing-Cheong Lo","doi":"10.1016/j.mbs.2025.109560","DOIUrl":"10.1016/j.mbs.2025.109560","url":null,"abstract":"<div><div>Interspecies interactions within ecosystems generate intricate ecological networks and spatial structures. To mitigate predation risks during ecological engagement, species frequently adopt adaptive survival strategies such as refuge concealment. This study develops a bi-trophic food-chain turbidostat model incorporating multiple time delays and refuge protection mechanisms to systematically investigate how critical parameters influence population dynamics and evolutionary patterns. Through rigorous stability analysis of system equilibria, we establish sufficient conditions for equilibrium stability and characterize parameter perturbation effects on system dynamics. Our bifurcation analysis reveals that both transcritical and Hopf bifurcations emerge when refuge parameters approach critical thresholds, demonstrating how parameter variations can transition population growth patterns from stable equilibrium to sustained oscillations. Notably, our refuge parameter analysis demonstrates the dual-edged nature of protective strategies: both excessive and insufficient refuge utilization destabilize population equilibrium. By employing center manifold and normal form theory, we quantitatively assess the nonlinear dynamics near bifurcation points and derive stability criteria for emergent periodic solutions. The temporal analysis further uncovers that time delays induce Hopf bifurcations when surpassing critical values, generating persistent population oscillations that endanger ecological stability. Numerical simulations across multiple parameter regimes consistently validate our theoretical predictions.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109560"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145288004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A two-phase model of early atherosclerotic plaque development with LDL toxicity effects 早期动脉粥样硬化斑块发展与LDL毒性作用的两阶段模型。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-10-06 DOI: 10.1016/j.mbs.2025.109547

Abdush Salam Pramanik , Bibaswan Dey , G.P. Raja Sekhar

{"title":"A two-phase model of early atherosclerotic plaque development with LDL toxicity effects","authors":"Abdush Salam Pramanik , Bibaswan Dey , G.P. Raja Sekhar","doi":"10.1016/j.mbs.2025.109547","DOIUrl":"10.1016/j.mbs.2025.109547","url":null,"abstract":"<div><div>Atherosclerosis is a chronic inflammatory cardiovascular disease in which fatty plaque builds up inside an artery wall. Early atherosclerotic plaque development is typically characterized by inflammatory tissue primarily consisting of macrophages and foam cells. In this article, we present a free boundary biphasic model of early atherosclerotic plaque to investigate the effects of low-density lipoprotein (LDL) toxicity on plaque development. The study examines the roles of cytokines (particularly monocyte chemoattractant protein-1) and oxidized low-density lipoprotein (oxLDL) in the recruitment of monocytes and the formation of foam cells, respectively. The ingestion of oxLDL by macrophages results in the accumulation of intracellular cholesterol, and its excessive level becomes toxic to foam cells, leading to cell death beyond a threshold. We examine how intracellular cholesterol-induced toxicity impacts plaque development. We find that the plaque initially grows rapidly, and the growth rate eventually declines due to cholesterol-induced toxicity. Parameters associated with toxicity-induced cell death play a key role in reducing the plaque growth rate by promoting cell death. We show that raising the toxicity threshold increases the volume fraction of inflammatory cells, thereby accelerating plaque growth. Investigations of the flux parameters reveal that increased cytokine flux enhances plaque growth, whereas higher oxLDL flux reduces the growth rate. A detailed analysis of the model presented in this article provides critical insights into the various biochemical and cellular mechanisms behind early plaque development.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109547"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145254331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Model formulation and oscillatory patterns in immune-pathogen dynamics during Brucellosis infection 布鲁氏菌感染期间免疫-病原体动力学的模型制定和振荡模式。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-12-01 Epub Date: 2025-09-30 DOI: 10.1016/j.mbs.2025.109543

Zehui Li , Junpeng Liu , Linhua Zhou , Chunhua Shan , Meng Fan

{"title":"Model formulation and oscillatory patterns in immune-pathogen dynamics during Brucellosis infection","authors":"Zehui Li , Junpeng Liu , Linhua Zhou , Chunhua Shan , Meng Fan","doi":"10.1016/j.mbs.2025.109543","DOIUrl":"10.1016/j.mbs.2025.109543","url":null,"abstract":"<div><div>Brucellosis, a global zoonosis imposing major health and economic burdens, is clinically marked by recurrent undulant fever linked to Brucella’s persistence within macrophages. To decipher the immune-pathogen dynamics underlying this fever periodicity, this study develops a novel mathematical model that integrates macrophage self-renewal, logistic growth constrained by cellular carrying capacity, and intracellular Brucella replication. Stability and bifurcation analyses reveal two crucial thresholds: one for infection persistence, requiring <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>, and another for the emergence of undulant fever, triggered by a supercritical Hopf bifurcation. This bifurcation occurs when the macrophage self-renewal rate (<span><math><mi>r</mi></math></span>) surpasses its mortality rate (<span><math><mi>d</mi></math></span>) and the infection rate (<span><math><mi>θ</mi></math></span>) lies in a critical range, marking a transition from stable equilibrium to stable limit cycles. These periodic oscillations, stemming from a dynamic imbalance between immune regeneration and bacterial proliferation, provide a direct mechanistic explanation for recurrent febrile episodes. Counterintuitively, excessive macrophage renewal or carrying capacity can destabilize the system, exacerbating febrile cycles. Our findings posit that interventions simultaneously preventing immune resource exhaustion and curbing intracellular bacterial survival could suppress these pathological oscillations, thereby proposing novel perspectives for managing chronic brucellosis.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109543"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145214835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0