Journal of Theoretical Biology最新文献

{"title":"Uncertainty Quantification in Cost-effectiveness Analysis for Stochastic-based Infectious Disease Models: Insights from Surveillance on Lymphatic Filariasis.","authors":"Mary Chriselda Antony Oliver, Matthew Graham, Ioanna Manolopoulou, Graham F Medley, Lorenzo Pellis, Koen B Pouwels, Matthew Thorpe, T Deirdre Hollingsworth","doi":"10.1016/j.jtbi.2025.112197","DOIUrl":"https://doi.org/10.1016/j.jtbi.2025.112197","url":null,"abstract":"<p><p>Cost-effectiveness analyses (CEA) typically involve comparing effectiveness and costs of one or more interventions compared to standard of care, to determine which intervention should be optimally implemented to maximise population health within the constraints of the healthcare budget. Traditionally, cost-effectiveness evaluations are expressed using incremental cost-effectiveness ratios (ICERs), which are compared with a fixed willingness-to-pay (WTP) threshold. Due to the existing uncertainty in costs for interventions and the overall burden of disease, particularly with regard to diseases in populations that are difficult to study, it becomes important to consider uncertainty quantification whilst estimating ICERs. To tackle the challenges of uncertainty quantification in CEA, we propose an alternative paradigm utilizing the Linear Wasserstein framework combined with Linear Discriminant Analysis (LDA) using a demonstrative example of lymphatic filariasis (LF). This approach uses geometric embeddings of the overall costs for treatment and surveillance, disability-adjusted lifeyears (DALYs) averted for morbidity by quantifying the burden of disease due to the years lived with disability, and probabilities of local elimination over a time-horizon of 20 years to evaluate the cost-effectiveness of lowering the stopping thresholds for post-surveillance determination of LF elimination as a public health problem. Our findings suggest that reducing the stopping threshold from <1% to <0.5% microfilaria (mf) prevalence for adults aged 20 years and above, under various treatment coverages and baseline prevalences, is cost-effective. When validated on 20% of test data, for 65% treatment coverage, a government expenditure of WTP ranging from $500 to $3,000 per 1% increase in local elimination probability justifies the switch to the lower threshold as cost-effective. Stochastic model simulations often lead to parameter and structural uncertainty in CEA. Uncertainty may impact the decisions taken, and this study underscores the necessity of better uncertainty quantification techniques within CEA for making informed decisions.</p>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":" ","pages":"112197"},"PeriodicalIF":1.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144369583","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}

{"title":"Modeling the effects of superoxide production on the cerebral blood flow.","authors":"David Terman, Yousef Hannawi","doi":"10.1016/j.jtbi.2025.112195","DOIUrl":"https://doi.org/10.1016/j.jtbi.2025.112195","url":null,"abstract":"<p><p>Oxidative stress with the associated endothelial cell dysfunction is an important pathophysiological mechanism for the hypertension induced vascular dysfunction and end organ damage. The oxidant stress leads to the impairment of nitric oxide synthesis, release and/or activity through multiple pathways which are all part of endothelial cells dysfunction. In the brain, this has been closely linked with the hypertension induced neurovascular dysfunction and impairment of cerebral blood flow regulation. The superoxide anion interacts with nitric oxide resulting in decreasing its bioavailability while generating the harmful perioxynitrite which contributes to the cellular oxidative damage. In this work, we develop a mathematical model representing the effects of nitric oxide and superoxide production and their interactions on changes of cerebral blood flow. Our model integrates and extends prior work through modeling the effects of nitric oxide and superoxide generation, diffusion and degradation on cerebral blood flow. Our results show that superoxide production attenuates the increase of cerebral blood flow mediated by nitric oxide production and explains the prior experimental observations. While strategies to increase nitric oxide production may alleviate the superoxide dependent decrease in cerebral blood flow, our model predicts an associated increase of perioxynitrite production leading to oxidative cellular injury. Our work provides a mathematical modeling platform that may be used to integrate the different cellular processes regulating the cellular response to oxidant stress. This platform can be utilized to test future therapeutics aiming to reduce the cerebrovascular oxidative stress related injuries and improve cerebral blood flow.</p>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":" ","pages":"112195"},"PeriodicalIF":1.9,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144340653","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}

{"title":"The role of nutrition in virus dynamics in vector-borne viral infections","authors":"Nora Heitzman-Breen ,&nbsp;Jacob Golden ,&nbsp;Yuyao Wang ,&nbsp;James Weger-Lucarelli ,&nbsp;Stanca M. Ciupe","doi":"10.1016/j.jtbi.2025.112184","DOIUrl":"10.1016/j.jtbi.2025.112184","url":null,"abstract":"<div><div>Malnutrition alters metabolism and immunity, affecting one’s ability to fight infections and influencing clinical outcomes. To quantify differences in infection dynamics among groups of different nutrition statuses and challenged with different viruses, we developed within-host mathematical models of acute infections and fitted them to data from mice fed either a high-fat overnutrition diet, a low-protein undernutrition diet, or a lean control diet and infected with either Mayaro, Ross River or chikungunya. In addition to finding virus-specific host-virus dynamics, model analyses showed decreased infected cell removal rates in undernourished infected mice compared to overnourished infected mice, regardless of the pathogen. Additionally, we found lower viral production rates in undernourished infected mice compared to overnourished infected mice, in two out of the three virus infections. These results suggest that diet is an important factor in understanding viral-host interactions, and should be considered when designing interventions.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112184"},"PeriodicalIF":1.9,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313607","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}

{"title":"Oscillation in the SIRS model","authors":"Davide Marenduzzo,&nbsp;Aidan T. Brown,&nbsp;Craig W. Miller,&nbsp;Graeme J. Ackland","doi":"10.1016/j.jtbi.2025.112169","DOIUrl":"10.1016/j.jtbi.2025.112169","url":null,"abstract":"<div><div>We study the SIRS epidemic model, both analytically and on a square lattice. The analytic model has two stable solutions, post outbreak/epidemic (no infected, <span><math><mrow><mi>I</mi><mo>=</mo><mn>0</mn></mrow></math></span>) and the endemic state (constant number of infected: <span><math><mrow><mi>I</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>). When the model is implemented with noise, or on a lattice, a third state is possible, featuring regular oscillations. This is understood as a cycle of boom and bust, where an epidemic sweeps through, and dies out leaving a small number of isolated infecteds. As immunity wanes, herd immunity is lost throughout the population and the epidemic repeats. The key result is that the oscillation is an intrinsic feature of the system itself, not driven by external factors such as seasonality or behavioural changes. The model shows that non-seasonal oscillations, such as those observed for the omicron COVID variant, need no additional explanation such as the appearance of more infectious variants at regular intervals or coupling to behaviour. We infer that the loss of immunity to the SARS-CoV-2 virus occurs on a timescale of about ten weeks.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112169"},"PeriodicalIF":1.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144295383","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}

{"title":"Modeling pesticide impacts on honey bee dynamics from mathematical and experimental integration","authors":"Jun Chen ,&nbsp;Adrian Fisher II ,&nbsp;Jon F. Harrison ,&nbsp;Gloria DeGrandi-Hoffman ,&nbsp;Jennifer H. Fewell ,&nbsp;Yun Kang","doi":"10.1016/j.jtbi.2025.112167","DOIUrl":"10.1016/j.jtbi.2025.112167","url":null,"abstract":"<div><div>Honey bees (Apis mellifera), essential pollinators, are critically affected by pesticides that contaminate pollen and are subsequently transported into their nests. In this study, we developed a delay differential equation model with age-specific structures, grounded in experimental data, to investigate the complex relationship between the pesticide Pristine®and honey bee population dynamics. The model enables the calculation of pollen consumption by both larvae and adults, offering deeper insights into the nutritional dynamics within hives. Our theoretical analysis revealed a significant direct linear relationship between egg and adult bee populations, determined by the ratio of adult-to-egg mortality rates, and the high death rate of adults decreases the colony population. The results indicate that adult mortality increases proportionally with pesticide concentration and alters the hive’s reproductive dynamics by shifting the timing of peak queen egg-laying. Simulations based on the model predict that high pesticide concentrations may lead to hive collapse, while control groups exhibit higher adult populations than treatment groups. These findings highlight the value of combining mathematical modeling with experimental data to understand and predict the complex effects of pesticides on honey bee populations, offering actionable insights for their conservation and management.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112167"},"PeriodicalIF":1.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321300","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}

{"title":"Fatty acids and physical activity are critical for β-cell mass and insulin sensitivity: Pathways to T2D and prevention","authors":"Rafiqul Islam ,&nbsp;Junyuan Yang ,&nbsp;Miao Li ,&nbsp;Sri Prakash Mokshagundam ,&nbsp;Lu Cai ,&nbsp;Jiaxu Li","doi":"10.1016/j.jtbi.2025.112188","DOIUrl":"10.1016/j.jtbi.2025.112188","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Existing mathematical models investigating the progression of type 2 diabetes (T2D) over time primarily focus on glucose, insulin, &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell mass, and other related factors, while often omitting fatty acids (FA) as an explicit variable—despite FA being a major energy source for the body. There exists a complex network of dynamical interactions among glucose, insulin, FA, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell mass. To gain deeper insights into the metabolic dynamics and pathophysiology of T2D, it is essential to incorporate FA into such models.&lt;/div&gt;&lt;div&gt;In this paper, we extend the classic Topp’s &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; model by explicitly incorporating FA and exploring its interactions with glucose, insulin, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell mass. A new formula for insulin sensitivity (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) is proposed to better capture the impaired effect of FA on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, enabling the exploration of diabetes development pathways and strategies for prevention or delay. Model simulations align well with clinical data and successfully replicate key characteristics of T2D progression, including declining &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, reduced &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell mass, a sedentary lifestyle, and excessive dietary intake. Our results demonstrate a strong positive correlation between glucose and FA levels, indicating that elevated FA is associated with increased glucose concentrations. Model analysis shows that FA levels in diabetic subjects rise significantly as a result of T2D development. Numerical analyses indicate that maintaining adequate physical activity or reducing dietary excess effectively preserves &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell mass, thereby reducing the risk of developing T2D.&lt;/div&gt;&lt;div&gt;Most notably, our detailed simulations reveal a striking pattern: in healthy and non-diabetic individuals, FA levels consistently remain below glucose levels across their lifespan. In contrast, in individuals with T2D, FA levels initially remain lower but begin to increase sharply and tangle with glucose levels, and then surpass glucose concentrations near the time of &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell failure. These patterns suggest that elevated FA may play a contributory role in increasing glucose levels, reducing insulin sensitivity, and ultimately leading to hyperglycemia. Our findings support the notion that glucotoxicity and lipotoxicity accelerate &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cell decline, impair insulin secretion, and drive T2D progression. Elevated FA thus emerges not only as a contributing pathway but also as a potential biomarker for monitoring disease development. Furthermore, the observed relationship betw","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112188"},"PeriodicalIF":1.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313606","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}

{"title":"Revisiting a demographic model of pest infestation in farming","authors":"Giuseppe Buffoni ,&nbsp;Sara Pasquali ,&nbsp;Cinzia Soresina","doi":"10.1016/j.jtbi.2025.112191","DOIUrl":"10.1016/j.jtbi.2025.112191","url":null,"abstract":"<div><div>Reliable simulations of pest population dynamics are essential tools for effective pest management. Here we present a demographic model designed to describe overwintering stage-structured population dynamics. In addition to accounting for development, mortality, and fecundity, the model explicitly incorporates diapause, a key physiological process enabling pests to survive winter conditions. We detail the formulation of the mortality rate function based on the development rate and the proportion of individuals dying within each developmental stage. Simulations are performed for the case of <em>Lobesia botrana</em>, a major vineyard pest. Results show, under both constant and fluctuating temperature regimes, the necessity of employing a density-dependent fecundity function to regulate population growth. Under constant temperature conditions, when fecundity depends on total population density, the system dynamics converge to a steady state regardless of the temporal discretization step, though peak values vary. Conversely, if fecundity is a function of adult density only, the model yields periodic oscillations. Under variable temperature regimes, diapause facilitates seasonal population resurgence and mitigates peak pupal and adult densities in the fall.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112191"},"PeriodicalIF":1.9,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144310768","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}

{"title":"Exploration of Hepatitis B Virus Infection Dynamics through an Intracellular Model","authors":"Rupchand Sutradhar,&nbsp;D.C. Dalal","doi":"10.1016/j.jtbi.2025.112189","DOIUrl":"10.1016/j.jtbi.2025.112189","url":null,"abstract":"<div><div>Analysis of the cell population generally provides average information about viral infection in a host whereas the intracellular model captures the individual cellular responses. The primary goal of this study is to comprehensively analyze the intracellular dynamics of hepatitis B virus (HBV) infection and to identify the most influential factors. In this study, an intracellular HBV infection dynamics model is proposed by considering several intracellular steps that are observed in the virus life cycle. Upon comparison with the experimental data, it is seen that the model solutions exhibit a good agreement. The well-known fourth-order <em>Runge-Kutta</em> method is applied to numerically solve the proposed model. The effects of HBx proteins, dslDNA-containing intermediates, intracellular delay and initial concentration of cccDNAs are explicitly studied. In order to identify the most positively and also the most negatively sensitive parameter of the proposed model, the global sensitivity analysis is performed using the widely-used method, Latin hypercube sampling-partial rank correlation coefficients. As a result, it is observed that HBx proteins have notable impacts on the dynamics of the infection, whereas intracellular delay and dslDNA-containing intermediates may not significantly affect the infection. This study also suggests that sub-viral particles could potentially contribute to the progression of the infection. Furthermore, recycling of capsids (an intracellular process perhaps unique to the HBV life cycle, where a portion of the newly produced capsids return to the nucleus and amplify the cccDNAs) is found to play an important role in enhancing the infection.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112189"},"PeriodicalIF":1.9,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144310767","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}

{"title":"Establishment of risk classification index for animal brucellosis by stochastic models","authors":"Liu Yang ,&nbsp;Qi Wang ,&nbsp;Youming Wang ,&nbsp;Meng Fan","doi":"10.1016/j.jtbi.2025.112187","DOIUrl":"10.1016/j.jtbi.2025.112187","url":null,"abstract":"<div><div>Brucellosis is a zoonotic disease of animal origin, which not only causes serious harm to the development of animal husbandry but also poses a threat to human health. Risk classification of animal brucellosis is very important and serves as the basis for decision-making of disease prevention and control. In this study, a probability model and continuous time Markov chain models are proposed to establish the importing probability and extinction probability for different production modes of farms, respectively. The main findings show that the importing probability has the most significant impact on the measures of quarantine and testing. For the extinction probability, when the environmental factors and indirect transmission are taken into account, the related parameters are sensitive, while the initial values of the infections are sensitive in the case that the environmental factors and indirect transmission are absent. Finally, the model is extended to the regional level and the data from epidemiological investigations are used to quantitatively assess the extinction probabilities of the three counties in a certain city.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112187"},"PeriodicalIF":1.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144303653","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}

{"title":"Selfish parents, altruistic children and helpers’ infertility","authors":"Ugo Pagano","doi":"10.1016/j.jtbi.2025.112190","DOIUrl":"10.1016/j.jtbi.2025.112190","url":null,"abstract":"<div><div>While Hamilton’s rule has traditionally attributed non-reproductive phenotypes to kin selection and altruistic behavior, we argue that infertile offspring can emerge through selfish parental resource allocation strategies without necessitating offspring altruism. By developing a model incorporating reproductive budget constraints, per-offspring investment costs, and fertility parameters, we derive the conditions under which producing infertile helpers optimizes parental fitness. The model predicts infertile phenotypes become evolutionarily advantageous when total offspring number exceeds a threshold or when per-offspring costs are sufficiently low. Parental optimization generates testable predictions differentiating it from pure altruism models, particularly the emergence of bimodal rather than continuous fertility distributions. The framework elucidates why sophisticated divisions of labor characterize species at opposite extremes of the offspring investment spectrum—social insects with minimal peroffspring costs and humans with exceptionally high investment—while remaining absent in species with intermediate investment levels. While parental optimization and Hamiltonian altruism represent distinct evolutionary pathways to helper infertility, we argue both mechanisms can be situated within inclusive fitness theory and may operate synergistically in natural populations.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"611 ","pages":"Article 112190"},"PeriodicalIF":1.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144303654","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}