Mathematical Biosciences and Engineering最新文献

筛选
英文 中文
A mathematical model for Zika virus disease: Intervention methods and control of affected pregnancies. 寨卡病毒病的数学模型:干预方法和受影响妊娠的控制。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-24 DOI: 10.3934/mbe.2025071
Chad Westphal, Shelby Stanhope, William Cooper, Cihang Wang
{"title":"A mathematical model for Zika virus disease: Intervention methods and control of affected pregnancies.","authors":"Chad Westphal, Shelby Stanhope, William Cooper, Cihang Wang","doi":"10.3934/mbe.2025071","DOIUrl":"10.3934/mbe.2025071","url":null,"abstract":"<p><p>Zika virus is spread to human populations primarily by Aedes aegypti mosquitoes, and Zika virus disease has been linked to a number of developmental abnormalities and miscarriages, generally coinciding with infection during early pregnancy. In this paper, we propose a new mathematical model for the transmission of Zika and study a range of control strategies to reduce the incidence of affected pregnancies in an outbreak. While most infectious disease models primarily focus on measures of the spread of the disease, our model is formulated to estimate the number of affected pregnancies throughout the simulated outbreak. Thus the effectiveness of control measures and parameter sensitivity analysis is done with respect to this metric. In addition to traditional intervention strategies, we consider the introduction of Wolbachia-infected mosquitoes into the native population. Our results suggest a threshold parameter for Wolbachia as an effective control measure, and show the natural time scale needed for Wolbachia-infected mosquitoes to effectively replace the native population. Additionally, we consider the possibility of a Zika vaccine, both to avoid an outbreak through herd immunity and as a control measure administered during an active outbreak. With emerging data on persistence of Zika virus in semen, the proposed compartmental model also includes a component of post-infectious males, which introduces a longer time scale for sexual transmission than the primary route. While the overall role of sexual transmission of Zika in an outbreak scenario is small compared with the dominant human-vector route, this model predicts conditions under which subpopulations may make this secondary route more significant.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 8","pages":"1956-1979"},"PeriodicalIF":2.6,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144976519","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}
引用次数: 0
Modelling behavioural interactions in infection disclosure during an outbreak: An evolutionary game theory approach. 暴发期间感染披露中的行为相互作用建模:进化博弈论方法。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-19 DOI: 10.3934/mbe.2025070
Pranav Verma, Viney Kumar, Samit Bhattacharyya
{"title":"Modelling behavioural interactions in infection disclosure during an outbreak: An evolutionary game theory approach.","authors":"Pranav Verma, Viney Kumar, Samit Bhattacharyya","doi":"10.3934/mbe.2025070","DOIUrl":"10.3934/mbe.2025070","url":null,"abstract":"<p><p>In confronting the critical challenge of disease outbreak management, health authorities consistently encourage individuals to voluntarily disclose a potential exposure to infection and adhere to self-quarantine protocols by assuring medical care (hospital beds, oxygen, and constant health monitoring) and helplines for severe patients. These have been observed during pandemics; for example, COVID-19 phases in many middle-income countries, such as India, promoted quarantine and reduced stigma. Here, we present a game-theoretic model to elucidate the behavioural interactions in infection disclosure during an outbreak. By employing a fractional derivative approach to model disease propagation, we determine the minimum level of voluntary disclosure required to disrupt the chain of transmission and allow the epidemic to fade. Our findings suggest that higher transmission rates and an increased perceived severity of infection may change the externality of the disclosing strategy, leading to an increase in the proportion of individuals who choose disclosure, and ultimately reducing disease incidence. We estimate the behavioural parameters and transmission rates by fitting the model to COVID-19 hospitalized cases in Chile, South America. The results from our paper underscore the potential for promoting the voluntary disclosure of infection during emerging outbreaks through effective risk communication, thereby emphasizing the severity of the disease and providing accurate information to the public about capacities within hospitals and medical care facilities.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 8","pages":"1931-1955"},"PeriodicalIF":2.6,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144976539","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}
引用次数: 0
Optimizing MDA and antimalarial treatment in the presence of drug resistance for effective malaria control. 在存在耐药性的情况下优化丙二醛和抗疟疾治疗,以有效控制疟疾。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-18 DOI: 10.3934/mbe.2025069
Manuela M Nimpa, Hyacinthe N Teytsa, Joseph Mbang, Charles S Wondji, Ramsès Djidjou-Demasse
{"title":"Optimizing MDA and antimalarial treatment in the presence of drug resistance for effective malaria control.","authors":"Manuela M Nimpa, Hyacinthe N Teytsa, Joseph Mbang, Charles S Wondji, Ramsès Djidjou-Demasse","doi":"10.3934/mbe.2025069","DOIUrl":"10.3934/mbe.2025069","url":null,"abstract":"<p><p>Antimalarial drugs are critical for controlling malaria, but the emergence of drug resistance poses a significant challenge to global eradication efforts. This study explores strategies to minimize resistance prevalence and improve malaria control, particularly through the use of mass drug administration (MDA) in combination with antimalarial drugs. We develop a compartmental mathematical model that incorporates asymptomatic, paucisymptomatic, and clinical states of infection and evaluates the impact of resistance mutations on transmission dynamics. The model includes both treated and untreated states among infected and recovered individuals, with a focus on optimizing control strategies through MDA and antimalarial treatment. A global sensitivity analysis identifies the critical factors that influence malaria dynamics, including MDA coverage, treatment access for different infection states, the probability of mutation from treated sensitive human infections, to treated resistant human infections and the initial prevalence of resistance. The model is extended to include optimal control strategies that provide time-dependent control interventions for treatment and MDA. Intuitively, when the mutation rate is relatively low, the optimal strategy combines the use of antimalarial drugs and MDA, with a gradual decrease in antimalarial drug use over time, ensuring sustainable malaria control. In contrast, at higher mutation rates, the strategy prioritizes broader deployment of MDA while significantly reducing reliance on antimalarial to minimize the risk of resistance developing. Numerical simulations of the optimal control problem reinforce the importance of strategic intervention in mitigating drug resistance. This study contributes to understanding the role of MDA and treatment strategies in the control of malaria, with implications for optimizing malaria control programs in endemic regions.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 8","pages":"1898-1930"},"PeriodicalIF":2.6,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144976477","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}
引用次数: 0
Equilibrium properties of a coupled contagion model of mosquito-borne disease and mosquito preventive behaviors. 蚊媒疾病与蚊虫预防行为耦合传染模型的平衡特性。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-18 DOI: 10.3934/mbe.2025068
Marya L Poterek, Mauricio Santos-Vega, T Alex Perkins
{"title":"Equilibrium properties of a coupled contagion model of mosquito-borne disease and mosquito preventive behaviors.","authors":"Marya L Poterek, Mauricio Santos-Vega, T Alex Perkins","doi":"10.3934/mbe.2025068","DOIUrl":"10.3934/mbe.2025068","url":null,"abstract":"<p><p>Although different strategies for mosquito-borne disease prevention can vary significantly in their efficacy and scale of implementation, they all require that individuals comply with their use. Despite this, human behavior is rarely considered in mathematical models of mosquito-borne diseases. Here, we sought to address that gap by establishing general expectations for how different behavioral stimuli and forms of mosquito prevention shape the equilibrium prevalence of disease. To accomplish this, we developed a coupled contagion model tailored to the epidemiology of dengue and preventive behaviors relevant to it. Under our model's parameterization, we found that mosquito biting was the most important driver of behavior uptake. In contrast, encounters with individuals experiencing disease or engaging in preventive behaviors themselves had a smaller influence on behavior uptake. The relative influence of these three stimuli reflected the relative frequency with which individuals encountered them. We also found that two distinct forms of mosquito prevention-namely, personal protection and mosquito density reduction-mediated different influences of behavior on equilibrium disease prevalence. Our results highlight that unique features of coupled contagion models can arise in disease systems with distinct biological features.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 8","pages":"1875-1897"},"PeriodicalIF":2.6,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144976462","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}
引用次数: 0
Massera's theorem on arbitrary discrete time domains. 任意离散时域上的Massera定理。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-06 DOI: 10.3934/mbe.2025067
Martin Bohner, Jaqueline G Mesquita, Sabrina Streipert
{"title":"Massera's theorem on arbitrary discrete time domains.","authors":"Martin Bohner, Jaqueline G Mesquita, Sabrina Streipert","doi":"10.3934/mbe.2025067","DOIUrl":"https://doi.org/10.3934/mbe.2025067","url":null,"abstract":"<p><p>We present a general version of Massera's theorems for arbitrary discrete domains, based on a newly introduced definition for both linear and nonlinear equations. For scalar nonlinear equations, we identify sufficient conditions that ensure each u-bounded solution approaches a periodic solution asymptotically. In the case of linear systems, we prove that the presence of a u-bounded solution necessarily leads to a periodic solution. We also provide some examples to show the practical implications of our findings.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1861-1874"},"PeriodicalIF":2.6,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660903","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}
引用次数: 0
Food choices and body weight changes: A mathematical model analysis. 食物选择与体重变化:数学模型分析。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-05 DOI: 10.3934/mbe.2025065
Mantana Chudtong, Andrea De Gaetano
{"title":"Food choices and body weight changes: A mathematical model analysis.","authors":"Mantana Chudtong, Andrea De Gaetano","doi":"10.3934/mbe.2025065","DOIUrl":"https://doi.org/10.3934/mbe.2025065","url":null,"abstract":"<p><p>A short-term stochastic model of minute-by-minute food intake is formulated, incorporating the interaction of appetite, insulinemia, and glycemia in determining the size and frequency of meals. By assuming a person would maintain his or her eating habit over time, we extend the simulation period to several years and explore scenarios based on food choices (high-fiber vs. high-carbohydrate) or appetite suppression. The model coherently predicts increments or decrements in body weight in the long-term when altering appetite in the short-term. Further, the model shows how food type choice, at the same appetite drive and habitual proposed meal size, induces macroscopic changes in body weight over a very few years. The model is innovative in that it connects the minute-by-minute behavior of the individual with long-term changes in metabolic compensation, in insulin sensitivity, in glycemic variability, and eventually in body size, thus helping to interpret the long-term development of Type 2 diabetes mellitus resulting from an unhealthy lifestyle.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1790-1824"},"PeriodicalIF":2.6,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660902","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}
引用次数: 0
Paramatrized intrusive POD-based reduced-order models applied to advection-diffusion-reaction problems. 基于参数化侵入式pod的降阶模型在平流扩散反应问题中的应用。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-06-05 DOI: 10.3934/mbe.2025066
P Solán-Fustero, J L Gracia, A Navas-Montilla, Pilar García-Navarro
{"title":"Paramatrized intrusive POD-based reduced-order models applied to advection-diffusion-reaction problems.","authors":"P Solán-Fustero, J L Gracia, A Navas-Montilla, Pilar García-Navarro","doi":"10.3934/mbe.2025066","DOIUrl":"https://doi.org/10.3934/mbe.2025066","url":null,"abstract":"<p><p>Parametrized problems involve high computational costs when looking for the proper values of their input parameters and solved with classical schemes. Reduced-order models (ROMs) based on the proper orthogonal decomposition act as alternative numerical schemes that speed up computational times while maintaining the accuracy of the solutions. They can be used to obtain solutions in a less expensive way for different values of the input parameters. The samples that compose the training set determine some computational limits on the solution that can be computed by the ROM. It is highly interesting to study what can be done to overcome these limits. In this article, the possibilities to obtain solutions to parametrized problems are explored and illustrated with several numerical cases using the two-dimensional (2D) advection-diffusion-reaction equation and the 2D wildfire propagation model.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1825-1860"},"PeriodicalIF":2.6,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660907","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}
引用次数: 0
Dynamic optimization of fishing tax and tourism fees for sustainable bioeconomic resource management. 面向可持续生物经济资源管理的渔业税收和旅游收费动态优化。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-05-28 DOI: 10.3934/mbe.2025064
Santanu Bhattacharya, Nandadulal Bairagi
{"title":"Dynamic optimization of fishing tax and tourism fees for sustainable bioeconomic resource management.","authors":"Santanu Bhattacharya, Nandadulal Bairagi","doi":"10.3934/mbe.2025064","DOIUrl":"https://doi.org/10.3934/mbe.2025064","url":null,"abstract":"<p><p>Balancing economic prosperity with environmental conservation is crucial in managing renewable bioeconomic resources. We explored a predator-prey fishery model that incorporates tourism, dynamic harvesting, and pricing strategies. Our analysis showed that increased fishing taxes reduce fishing efforts, enabling fish populations to recover. Furthermore, higher entrance fees for ecotourism support the predator population's growth. Bifurcation analysis revealed key dynamic transitions, including transcritical and Hopf bifurcations. A deeper look into coupled parameter bifurcation uncovered a transcritical bifurcation of the limit cycle, emphasizing the system's complexity. Using Pontryagin's maximum principle, we optimized fishing taxes and ecotourism entrance fees to achieve sustainable trade-offs between ecosystem health and societal revenue. The results highlighted that societal revenue peaked at an intermediate level of entrance fees, suggesting diminishing returns beyond a certain point. Revenue landscape analysis further showed that centralized, two-parameter optimization strategies outperform decentralized, single-parameter approaches. These insights provide policymakers with effective tools to design regulations that promote ecological resilience and economic viability through balanced fishing and tourism practices.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1751-1789"},"PeriodicalIF":2.6,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660901","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}
引用次数: 0
Modeling the impact of temperature on the dynamics of carrier-dependent infectious diseases with control strategies. 用控制策略模拟温度对载体依赖性传染病动力学的影响。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-05-28 DOI: 10.3934/mbe.2025063
Shubham Chaudhry, Gauri Agrawal, Maia Martcheva, A K Misra
{"title":"Modeling the impact of temperature on the dynamics of carrier-dependent infectious diseases with control strategies.","authors":"Shubham Chaudhry, Gauri Agrawal, Maia Martcheva, A K Misra","doi":"10.3934/mbe.2025063","DOIUrl":"https://doi.org/10.3934/mbe.2025063","url":null,"abstract":"<p><p>The spread of diseases poses significant threats to human health globally. The dynamic nature of infectious diseases, especially those that also rely on carriers (e.g., house flies) for transmission, requires innovative strategies to control their spread, as environmental conditions such as temperature, humidity, etc., affect the rate of growth of the carrier population. This study introduces a mathematical model to assess the effect of increasing global average temperature rise caused by carbon dioxide emissions and chemical control strategies on the dynamics of such diseases. The stability properties of feasible equilibrium solutions were discussed. Sensitivity analysis was also performed to highlight the key parameters that may help to design effective intervention strategies to control disease transmission. The model was further analyzed for an optimal control problem by incorporating a control measure on the application rate of chemical insecticides to reduce the carrier population. Through the combination of analytical techniques and numerical simulations, we have evaluated the effectiveness of chemical control strategies under varying epidemiological parameters. The model also explored the critical thresholds necessary for achieving disease control and eradication. Our results are valuable to public health officials and policymakers in designing effective interventions against carrier-dependent infectious diseases.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1722-1750"},"PeriodicalIF":2.6,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660904","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}
引用次数: 0
Challenges in the mathematical modeling of the spatial diffusion of SARS-CoV-2 in Chile. 智利SARS-CoV-2空间扩散数学建模面临的挑战。
IF 2.6 4区 工程技术
Mathematical Biosciences and Engineering Pub Date : 2025-05-27 DOI: 10.3934/mbe.2025062
Gilberto González-Parra, Cristina-Luisovna Pérez, Marcos Llamazares, Rafael-J Villanueva, Jesus Villegas-Villanueva
{"title":"Challenges in the mathematical modeling of the spatial diffusion of SARS-CoV-2 in Chile.","authors":"Gilberto González-Parra, Cristina-Luisovna Pérez, Marcos Llamazares, Rafael-J Villanueva, Jesus Villegas-Villanueva","doi":"10.3934/mbe.2025062","DOIUrl":"10.3934/mbe.2025062","url":null,"abstract":"<p><p>We propose several spatial-temporal epidemiological mathematical models to study their suitability to approximate the dynamics of the early phase of the COVID-19 pandemic in Chile. The model considers the population density of susceptible, infected, and recovered individuals. The models are based on a system of partial differential equations. The first model considers a space-invariant transmission rate, and the second modeling approach is based on different space-variant transmission rates. The third modeling approach, which is more complex, uses a transmission rate that varies with space and time. One main aim of this study is to present the advantages and drawbacks of the mathematical approaches proposed to describe the COVID-19 pandemic in Chile. We show that the calibration of the models is challenging. The results of the model's calibration suggest that the spread of SARS-CoV-2 in the regions of Chile was different. Moreover, this study provides additional insight since few studies have explored similar mathematical modeling approaches with real-world data.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 7","pages":"1680-1721"},"PeriodicalIF":2.6,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12358164/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144660900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信