Bulletin of Mathematical Biology最新文献_第2页

Correction: Stochastic Models of Zoonotic Avian Influenza with Multiple Hosts, Environmental Transmission, and Migration in the Natural Reservoir.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-24 DOI: 10.1007/s11538-025-01428-y

Rowan L Hassman, Iona M H McCabe, Kaia M Smith, Linda J S Allen

引用次数: 0

Vaccination and Collective Action Under Social Norms. 社会规范下的疫苗接种和集体行动。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-24 DOI: 10.1007/s11538-025-01436-y

Bryce Morsky

{"title":"Vaccination and Collective Action Under Social Norms.","authors":"Bryce Morsky","doi":"10.1007/s11538-025-01436-y","DOIUrl":"https://doi.org/10.1007/s11538-025-01436-y","url":null,"abstract":"Social dynamics are an integral part of the spread of disease affecting contact rates as well as the adoption of pharmaceutical and non-pharmaceutical interventions. When vaccines provide waning immunity, efficient and timely uptake of boosters is required to maintain protection and reduce infections. How then do social dynamics affect the timely uptake of vaccines and thereby the course of an epidemic? This paper explores this scenario through a behavioural-epidemiological model. It features a tipping-point dynamic for the uptake of vaccines that combines the risk of infection, perceived morbidity risk of the vaccine, and social payoffs for deviating from the vaccination decision-making of others. The social payoffs are derived from a social norm of conformity, and they create a collective action problem. A key finding driven by this dilemma is that waves of vaccine uptake and infections can occur due to inefficient and delayed uptake of boosters. This results in a nonlinear response of the infection load to the transmission rate: an intermediate transmission rate can result in greater prevalence of disease relative to more or less transmissible diseases. Further, global information about the prevalence of the disease and vaccine uptake can increase the infection load and peak relative to information restricted to individuals' contact networks. Thus, decisions driven by local information can mitigate the collective action problem across the population. Finally, the optimal public policy program to promote boosters is shown to be one that focuses on overcoming the social inertia to vaccinate at the start of an epidemic.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"55"},"PeriodicalIF":2.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699768","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

Mathematical Modelling of the First HIV/ZIKV Co-infection Cases in Colombia and Brazil.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-21 DOI: 10.1007/s11538-025-01429-x

Jhoana P Romero-Leiton, Idriss Sekkak, Julien Arino, Iain Moyles, Bouchra Nasri

{"title":"Mathematical Modelling of the First HIV/ZIKV Co-infection Cases in Colombia and Brazil.","authors":"Jhoana P Romero-Leiton, Idriss Sekkak, Julien Arino, Iain Moyles, Bouchra Nasri","doi":"10.1007/s11538-025-01429-x","DOIUrl":"https://doi.org/10.1007/s11538-025-01429-x","url":null,"abstract":"This paper presents a mathematical model to investigate the co-infection with human immunodeficiency virus (HIV) and Zika virus (ZIKV) in Colombia and Brazil, where the first cases were reported in 2015. The model considers the sexual transmission dynamics of both viruses and vector-host interactions. We begin by exploring the qualitative behaviour of each model separately. We then analyze the dynamics of the co-infection model using the thresholds and results defined separately for each model. The model also considers the impact of intervention strategies, such as personal protection, antiretroviral therapy (ART), and sexual protection (condom use). Using available and assumed parameter values for Colombia and Brazil, the model is calibrated to investigate the long-term co-infection dynamics, the influence of specific parameters, and the potential effect of implementing these intervention strategies on co-infection spread. The study's results revealed that the duration of Zika infection is a critical factor influencing the burden of co-infection cases. Additionally, bed nets and use of condoms are essential for disease control, while ART is less emphasized due to the cost-effectiveness of condom use.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"54"},"PeriodicalIF":2.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143673386","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 Mathematical Exploration of SDH-b Loss in Chromaffin Cells.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-13 DOI: 10.1007/s11538-025-01427-z

Elías Vera-Sigüenza, Himani Rana, Ramin Nashebi, Ielyaas Cloete, Katarína Kl'uvčková, Fabian Spill, Daniel A Tennant

{"title":"A Mathematical Exploration of SDH-b Loss in Chromaffin Cells.","authors":"Elías Vera-Sigüenza, Himani Rana, Ramin Nashebi, Ielyaas Cloete, Katarína Kl'uvčková, Fabian Spill, Daniel A Tennant","doi":"10.1007/s11538-025-01427-z","DOIUrl":"10.1007/s11538-025-01427-z","url":null,"abstract":"The succinate dehydrogenase (SDH) is a four-subunit enzyme complex (SDH-a, SDH-b, SDH-c, and SDH-d) central to cell carbon metabolism. The SDH bridges the tricarboxylic acid cycle to the electron transport chain. A pathological loss of the SDH-b subunit leads to a cell-wide signalling cascade that shifts the cell's metabolism into a pseudo-hypoxic state akin to the so-called Warburg effect (or aerobic glycolysis). This trait is a hallmark of phaeochromocytomas, a rare tumour arising from chromaffin cells; a type of cell that lies in the medulla of the adrenal gland. In this study, we leverage the insights from a mathematical model constructed to underpin the metabolic implications of SDH-b dysfunction in phaeochromocytomas. We specifically investigate why chromaffin cells seemingly have the ability to maintain electron transport chain's Complex I function when confronted with the loss of the SDH-b subunit while other cells do not. Our simulations indicate that retention of Complex I is associated with cofactor oxidation, which enables cells to manage mitochondrial swelling and limit the reversal of the adenosine triphosphate synthase, supporting cell fitness, without undergoing lysis. These results support previous hypotheses that point to mitochondrial proton leaks as a critical factor of future research. Moreover, the model asserts that control of the proton gradient across the mitochondrial inner membrane is rate-limiting upon fitness management of SDH-b deficient cells.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"53"},"PeriodicalIF":2.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11906556/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143623523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Characterization of the Long-distance Dispersal Kernel of White-Tailed Deer and Evaluating its Impact on Chronic Wasting Disease Spread in Wisconsin. 白尾鹿长距离传播内核的特征及其对威斯康星州慢性消耗性疾病传播的影响评估。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-13 DOI: 10.1007/s11538-024-01394-x

Mennatallah Gouda, Jim Powell, W Jacob McClure, Daniel P Walsh, Daniel Storm

{"title":"Characterization of the Long-distance Dispersal Kernel of White-Tailed Deer and Evaluating its Impact on Chronic Wasting Disease Spread in Wisconsin.","authors":"Mennatallah Gouda, Jim Powell, W Jacob McClure, Daniel P Walsh, Daniel Storm","doi":"10.1007/s11538-024-01394-x","DOIUrl":"10.1007/s11538-024-01394-x","url":null,"abstract":"Chronic wasting disease (CWD) is a fatal neurodegenerative disease infecting cervids. It is highly contagious and caused by misfolded prions that propagate via templated conformational conversion of the cervid's normal prion protein. Prevalence of CWD in free-ranging deer in North America is mostly low, but in some regions local prevalence has reached 80%. CWD prions can be transmitted via direct contact with infected individuals or indirectly through the environment. Infected individuals shed prions through feces, urine, saliva or carcasses, and prions have long environmental persistence. Long-distance dispersal of infected deer poses a significant risk for CWD spread. We propose an integrodifference equation (IDE) model to capture CWD dynamics and the consequences of long-distance dispersal behavior in white-tailed deer (WTD, Odocoileus virginianus). A diffusion-settling model characterizes long-distance dispersal kernels, accommodating hypothetical dispersal behaviors through time-dependent settling rate functions. Three new closed-form dispersal kernels are approximated using Laplace's method and parameterized with GPS location data collected from WTD in Wisconsin, USA. Settling rates reflecting ongoing sensitivity to stimuli which prompt deer to disperse from their natal home range give the most supported long-distance dispersal kernel. Impact of long-distance dispersal on CWD spread is quantified using the IDE model. At high population densities, long-distance dispersal can magnify CWD spread by a factor of four. At lower population densities single infected individuals cannot initiate an outbreak, but CWD may still spread due to the accumulation of environmental hazard from prions behind the wave of invasion, possibly presenting substantial management challenges.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"52"},"PeriodicalIF":2.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143623671","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

Exploring the Evolution of Altruistic Punishment with a PDE Model of Cultural Multilevel Selection.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-12 DOI: 10.1007/s11538-025-01422-4

Daniel B Cooney

{"title":"Exploring the Evolution of Altruistic Punishment with a PDE Model of Cultural Multilevel Selection.","authors":"Daniel B Cooney","doi":"10.1007/s11538-025-01422-4","DOIUrl":"10.1007/s11538-025-01422-4","url":null,"abstract":"Two mechanisms that have been used to study the evolution of cooperative behavior are altruistic punishment, in which cooperative individuals pay additional costs to punish defection, and multilevel selection, in which competition between groups can help to counteract individual-level incentives to cheat. Boyd, Gintis, Bowles, and Richerson have used simulation models of cultural evolution to suggest that altruistic punishment and pairwise group-level competition can work in concert to promote cooperation, even when neither mechanism can do so on its own. In this paper, we formulate a PDE model for multilevel selection motivated by the approach of Boyd and coauthors, modeling individual-level birth-death competition with a replicator equation based on individual payoffs and describing group-level competition with pairwise conflicts based on differences in the average payoffs of the competing groups. Building off of existing PDE models for multilevel selection with frequency-independent group-level competition, we use analytical and numerical techniques to understand how the forms of individual and average payoffs can impact the long-time ability to sustain altruistic punishment in group-structured populations. We find several interesting differences between the behavior of our new PDE model with pairwise group-level competition and existing multilevel PDE models, including the observation that our new model can feature a non-monotonic dependence of the long-time collective payoff on the strength of altruistic punishment. Going forward, our PDE framework can serve as a way to connect and compare disparate approaches for understanding multilevel selection across the literature in evolutionary biology and anthropology.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"51"},"PeriodicalIF":2.0,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143613490","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

Epidemiological Dynamics in Populations Structured by Neighbourhoods and Households.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-27 DOI: 10.1007/s11538-025-01426-0

Abby Barlow, Sarah Penington, Ben Adams

{"title":"Epidemiological Dynamics in Populations Structured by Neighbourhoods and Households.","authors":"Abby Barlow, Sarah Penington, Ben Adams","doi":"10.1007/s11538-025-01426-0","DOIUrl":"10.1007/s11538-025-01426-0","url":null,"abstract":"Epidemiological dynamics are affected by the spatial and demographic structure of the host population. Households and neighbourhoods are known to be important groupings but little is known about the epidemiological interplay between them. In order to explore the implications for infectious disease epidemiology of households with similar demographic structures clustered in space we develop a multi-scale epidemic model consisting of neighbourhoods of households. In our analysis we focus on key parameters which control household size, the importance of transmission within households relative to outside of them, and the degree to which the non-household transmission is localised within neighbourhoods. We construct the household reproduction number <math><mmultiscripts><mi>R</mi> <mrow><mrow></mrow> <mo>∗</mo></mrow> <mrow></mrow></mmultiscripts> </math> over all neighbourhoods and derive the analytic probability of an outbreak occurring from a single infected individual in a specific neighbourhood. We find that reduced localisation of transmission within neighbourhoods reduces <math><mmultiscripts><mi>R</mi> <mrow><mrow></mrow> <mo>∗</mo></mrow> <mrow></mrow></mmultiscripts> </math> when household size differs between neighbourhoods. This effect is amplified by larger differences between household sizes and larger divergence between transmission rates within households and outside of them. However, the impact of neighbourhoods with larger household sizes on an individual's risk of infection is mainly limited to the individuals that reside in those neighbourhoods. We consider various surveillance scenarios and show that household size information from the initial infectious cases is often more important than neighbourhood information while household size and neighbourhood localisation influences the sequence of neighbourhoods in which an outbreak is observed.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"50"},"PeriodicalIF":2.0,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11868190/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143522736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains. 增长的一维域上反应-扩散模式的尖峰自复制和尖峰成核的渐近分析。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-24 DOI: 10.1007/s11538-025-01418-0

Chunyi Gai, Edgardo Villar-Sepúlveda, Alan Champneys, Michael J Ward

{"title":"An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains.","authors":"Chunyi Gai, Edgardo Villar-Sepúlveda, Alan Champneys, Michael J Ward","doi":"10.1007/s11538-025-01418-0","DOIUrl":"10.1007/s11538-025-01418-0","url":null,"abstract":"In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a one-dimensional finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinct bifurcation mechanisms can occur which generate spike patterns of increased spatial complexity as the domain half-length L slowly increases; so-called spike nucleation and spike self-replication. Self-replication is found to occur via the passage beyond a saddle-node bifurcation point that can be predicted through linearization around the inner spike profile. In contrast, spike nucleation occurs through slow passage beyond the saddle-node of a nonlinear boundary-value problem defined in the outer region away from the core of a spike. Here, by treating L as a static parameter under the Lagrangian framework, precise conditions are established within the semi-strong interaction asymptotic regime to determine which occurs, conditions that are confirmed by numerical simulation and continuation. For the Schnakenberg and Brusselator RD models, phase diagrams in parameter space are derived that predict whether spike self-replication or spike nucleation will occur first as L is increased, or whether no such instability will occur. For the Gierer-Meinhardt model with a non-trivial activator background, spike nucleation is shown to be the only possible spike-generating mechanism. From time-dependent PDE numerical results on an exponentially slowly growing domain, it is shown that the analytical thresholds derived from the asymptotic theory accurately predict critical values of L where either spike self-replication or spike-nucleation will occur. The global bifurcation mechanism for transitions to patterns of increased spatial complexity is further elucidated by superimposing time-dependent PDE simulation results on the numerically computed solution branches of spike equilibria in which L is the primary bifurcation parameter.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"48"},"PeriodicalIF":2.0,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481833","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

EAD Mechanisms in Hypertrophic Mouse Ventricular Myocytes: Insights from a Compartmentalized Mathematical Model.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-24 DOI: 10.1007/s11538-025-01423-3

Dilmini Warnakulasooriya, Vladimir E Bondarenko

{"title":"EAD Mechanisms in Hypertrophic Mouse Ventricular Myocytes: Insights from a Compartmentalized Mathematical Model.","authors":"Dilmini Warnakulasooriya, Vladimir E Bondarenko","doi":"10.1007/s11538-025-01423-3","DOIUrl":"10.1007/s11538-025-01423-3","url":null,"abstract":"Transverse aortic constriction (TAC) is one of the experimental mouse models that are designed to investigate cardiac hypertrophy and heart failure. Most of the studies with this model are devoted to the stage of developed heart failure. However, several studies of the early stages (hypertrophy after 1 week of TAC) of this disease found significant changes in the β-adrenergic system, electrical activity, and Ca2+ dynamics in mouse ventricular myocytes. To provide a quantitative description of cardiac hypertrophy, we developed a new compartmentalized mathematical model of hypertrophic mouse ventricular myocytes for the early stage after the TAC procedure. The model described the changes in cell geometry, action potentials, [Ca2+]i transients, and β1- and β2-adrenergic signaling systems. We also showed that the hypertrophic myocytes demonstrated early afterdepolarizations (EADs) upon stimulation with isoproterenol at relatively long stimulation periods. Simulation of the hypertrophic myocyte activities revealed that the synergistic effects of the late Na+ current, the L-type Ca2+ current, and the T-type Ca2+ current were responsible for the initiation of EADs. The mechanisms of EAD and its suppression were investigated and sensitivity analysis was performed. Simulation results obtained with the hypertrophic cell model were compared to those from the normal ventricular myocytes. The developed mathematical model can be used for the explanation of the existing experimental data, for the development of the models for other hypertrophic phenotypes, and to make experimentally testable predictions of a hypertrophic myocyte's behavior.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"49"},"PeriodicalIF":2.0,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481835","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

modelSSE: An R Package for Characterizing Infectious Disease Superspreading from Contact Tracing Data. modelSSE：从接触追踪数据描述传染病超级传播特征的 R 软件包。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-21 DOI: 10.1007/s11538-025-01421-5

Shi Zhao, Zihao Guo, Kai Wang, Shengzhi Sun, Dayu Sun, Weiming Wang, Daihai He, Marc Kc Chong, Yuantao Hao, Eng-Kiong Yeoh

{"title":"modelSSE: An R Package for Characterizing Infectious Disease Superspreading from Contact Tracing Data.","authors":"Shi Zhao, Zihao Guo, Kai Wang, Shengzhi Sun, Dayu Sun, Weiming Wang, Daihai He, Marc Kc Chong, Yuantao Hao, Eng-Kiong Yeoh","doi":"10.1007/s11538-025-01421-5","DOIUrl":"10.1007/s11538-025-01421-5","url":null,"abstract":"Infectious disease superspreading is a phenomenon where few primary cases generate unexpectedly large numbers of secondary cases. Superspreading, is frequently documented in epidemiology literature, and is considered a consequence of heterogeneity in transmission. Since understanding the risks of superspreading became a rising concern from both statistical modelling and public health aspects, the R package modelSSE provides comprehensive analytical tools to characterize transmission heterogeneity. The package modelSSE integrates recent advances in statistical methods, such as decomposition of reproduction number, for modelling infectious disease superspreading using various types and sources of contact tracing data that allow models to be grounded in real-world observations. This study provided an overview of the theoretical background and implementation of modelSSE, designed to facilitate learning infectious disease transmission, and explore novel research questions for transmission risks and superspreading potentials. Detailed examples of classic, historical infectious disease datasets are given for demonstration and model extensions.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"47"},"PeriodicalIF":2.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143467161","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