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- [1] Reconstruction of the transmission dynamics of the first COVID-19 epidemic wave in ThailandSCIENTIFIC REPORTS, 2022, 12 (01)Wilasang, Chaiwat论文数: 0 引用数: 0 h-index: 0机构: Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, Thailand Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, ThailandJitsuk, Natcha C.论文数: 0 引用数: 0 h-index: 0机构: Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, Thailand Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, ThailandSararat, Chayanin论文数: 0 引用数: 0 h-index: 0机构: Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, Thailand Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, ThailandModchang, Charin论文数: 0 引用数: 0 h-index: 0机构: Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, Thailand Ctr Excellence Math, CHE, Bangkok 10400, Thailand CHE, Thailand Ctr Excellence Phys, 328 Si Ayutthaya Rd, Bangkok 10400, Thailand Mahidol Univ, Fac Sci, Dept Phys, Biophys Grp, Bangkok 10400, Thailand
- [2] Transmission dynamics of the COVID-19 epidemic in EnglandINTERNATIONAL JOURNAL OF INFECTIOUS DISEASES, 2021, 104 : 132 - 138Liu, Yang论文数: 0 引用数: 0 h-index: 0机构: Univ Cambridge, Sch Clin Med, Med Res Council, Biostat Unit, Cambridge, England Univ Cambridge, Sch Clin Med, Med Res Council, Biostat Unit, Cambridge, EnglandTang, Julian W.论文数: 0 引用数: 0 h-index: 0机构: Univ Leicester, Resp Sci, Leicester, Leics, England Univ Cambridge, Sch Clin Med, Med Res Council, Biostat Unit, Cambridge, EnglandLam, Tommy T. Y.论文数: 0 引用数: 0 h-index: 0机构: Univ Hong Kong, Sch Publ Hlth, State Key Lab Emerging Infect Dis, Hong Kong, Peoples R China Univ Cambridge, Sch Clin Med, Med Res Council, Biostat Unit, Cambridge, England
- [3] Modeling the Transmission Dynamics of the COVID-19 Outbreak in ThailandTHAI JOURNAL OF MATHEMATICS, 2020, 18 (04): : 1907 - 1915Thawinan, Ekkachai论文数: 0 引用数: 0 h-index: 0机构: Chiang Mai Univ, Fac Sci, Dept Math, Chiang Mai, Thailand Chiang Mai Univ, Fac Sci, Dept Math, Res Ctr Math & Appl Math, Chiang Mai, Thailand Chiang Mai Univ, Fac Sci, Dept Math, Chiang Mai, Thailand论文数: 引用数: h-index:机构:
- [4] COVID-19 transmission dynamics underlying epidemic waves in KenyaSCIENCE, 2021, 374 (6570) : 989 - +Brand, Samuel P. C.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Univ Warwick, Zeeman Inst Syst Biol & Infect Dis Epidemiol Res, Warwick, England Univ Warwick, Sch Life Sci, Warwick, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOjal, John论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya London Sch Hyg & Trop Med LSHTM, London, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAziza, Rabia论文数: 0 引用数: 0 h-index: 0机构: Univ Warwick, Zeeman Inst Syst Biol & Infect Dis Epidemiol Res, Warwick, England Univ Warwick, Sch Life Sci, Warwick, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaWere, Vincent论文数: 0 引用数: 0 h-index: 0机构: KEMRI Wellcome Trust Res Programme, Hlth Econ Res Unit, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOkiro, Emelda A.论文数: 0 引用数: 0 h-index: 0机构: Kenya Govt Med Res Ctr, Populat Hlth Unit, Wellcome Trust Res Programme, Nairobi, Kenya Univ Oxford, Ctr Trop Med & Global Hlth, Nuffield Dept Med, Oxford, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaKombe, Ivy K.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaMburu, Caroline论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOgero, Morris论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAgweyu, Ambrose论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Univ Oxford, Ctr Trop Med & Global Hlth, Nuffield Dept Med, Oxford, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaWarimwe, George M.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Univ Oxford, Ctr Trop Med & Global Hlth, Nuffield Dept Med, Oxford, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaNyagwange, James论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaKaranja, Henry论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaGitonga, John N.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaMugo, Daisy论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaUyoga, Sophie论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAdetifa, Ifedayo M. O.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya London Sch Hyg & Trop Med, Dept Infect Dis Epidemiol, London, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaScott, J. Anthony G.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya London Sch Hyg & Trop Med, Dept Infect Dis Epidemiol, London, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOtieno, Edward论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaMurunga, Nickson论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOtiende, Mark论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaOchola-Oyier, Lynette, I论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAgoti, Charles N.论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaGithinji, George论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaKasera, Kadondi论文数: 0 引用数: 0 h-index: 0机构: Govt Kenya, Minist Hlth, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAmoth, Patrick论文数: 0 引用数: 0 h-index: 0机构: Govt Kenya, Minist Hlth, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaMwangangi, Mercy论文数: 0 引用数: 0 h-index: 0机构: Govt Kenya, Minist Hlth, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaAman, Rashid论文数: 0 引用数: 0 h-index: 0机构: Govt Kenya, Minist Hlth, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaNg'ang'a, Wangari论文数: 0 引用数: 0 h-index: 0机构: Govt Kenya, Presidential Policy & Strategy Unit, Presidency, Nairobi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaTsofa, Benjamin论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya论文数: 引用数: h-index:机构:Keeling, Matt J.论文数: 0 引用数: 0 h-index: 0机构: Univ Warwick, Zeeman Inst Syst Biol & Infect Dis Epidemiol Res, Warwick, England Univ Warwick, Sch Life Sci, Warwick, England Univ Warwick, Math Inst, Warwick, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaNokes, D. James论文数: 0 引用数: 0 h-index: 0机构: Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya Univ Warwick, Zeeman Inst Syst Biol & Infect Dis Epidemiol Res, Warwick, England Univ Warwick, Sch Life Sci, Warwick, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, KenyaBarasa, Edwine论文数: 0 引用数: 0 h-index: 0机构: KEMRI Wellcome Trust Res Programme, Hlth Econ Res Unit, Nairobi, Kenya Univ Oxford, Ctr Trop Med & Global Hlth, Nuffield Dept Med, Oxford, England Kenya Med Res Inst KEMRI, Wellcome Trust Res Programme KWTRP, Kilifi, Kenya
- [5] Modeling the transmission dynamics of COVID-19 epidemic: a systematic reviewJOURNAL OF BIOMEDICAL RESEARCH, 2020, 34 (06): : 422 - 430Guan, Jinxing论文数: 0 引用数: 0 h-index: 0机构: Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R China Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R ChinaWei, Yongyue论文数: 0 引用数: 0 h-index: 0机构: Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R China Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R ChinaZhao, Yang论文数: 0 引用数: 0 h-index: 0机构: Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R China Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R ChinaChen, Feng论文数: 0 引用数: 0 h-index: 0机构: Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R China Nanjing Med Univ, Ctr Global Hlth, Sch Publ Hlth, Dept Epidemiol & Biostat, 101 Longmian Ave, Nanjing 211166, Jiangsu, Peoples R China
- [6] A COVID-19 epidemic model with periodicity in transmission and environmental dynamicsFRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2023, 9Assan, Belthasara论文数: 0 引用数: 0 h-index: 0机构: Univ Johannesburg, Dept Math & Appl Math, Johannesburg, South Africa Univ Johannesburg, Dept Math & Appl Math, Johannesburg, South AfricaNyabadza, Farai论文数: 0 引用数: 0 h-index: 0机构: Univ Johannesburg, Dept Math & Appl Math, Johannesburg, South Africa Emirates Aviat Univ, Inst Appl Res & Technol, Dubai, U Arab Emirates Univ Johannesburg, Dept Math & Appl Math, Johannesburg, South Africa
- [7] Modeling the transmission dynamics of COVID-19 epidemic:a systematic reviewTheJournalofBiomedicalResearch, 2020, 34 (06) : 422 - 430Jinxing Guan论文数: 0 引用数: 0 h-index: 0机构: Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical University Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical UniversityYongyue Wei论文数: 0 引用数: 0 h-index: 0机构: Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical University Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical UniversityYang Zhao论文数: 0 引用数: 0 h-index: 0机构: Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical University Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical UniversityFeng Chen论文数: 0 引用数: 0 h-index: 0机构: Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical University Department of Epidemiology and Biostatistics,School of Public Health,Center for Global Health,Nanjing Medical University
- [8] Reconstruction of the full transmission dynamics of COVID-19 in WuhanNature, 2020, 584 : 420 - 424Xingjie Hao论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical CollegeShanshan Cheng论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical CollegeDegang Wu论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical CollegeTangchun Wu论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical CollegeXihong Lin论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical CollegeChaolong Wang论文数: 0 引用数: 0 h-index: 0机构: Huazhong University of Science and Technology,Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical College
- [9] Reconstruction of the full transmission dynamics of COVID-19 in WuhanNATURE, 2020, 584 (7821) : 420 - +Hao, Xingjie论文数: 0 引用数: 0 h-index: 0机构: Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Dept Epidemiol & Biostat, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R ChinaCheng, Shanshan论文数: 0 引用数: 0 h-index: 0机构: Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Dept Epidemiol & Biostat, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R ChinaWu, Degang论文数: 0 引用数: 0 h-index: 0机构: Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Dept Epidemiol & Biostat, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R ChinaWu, Tangchun论文数: 0 引用数: 0 h-index: 0机构: Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Dept Occupat & Environm Hlth, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Natl Med Ctr Major Publ Hlth Events, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R ChinaLin, Xihong论文数: 0 引用数: 0 h-index: 0机构: Harvard TH Chan Sch Publ Hlth, Dept Biostat, Boston, MA 02115 USA Harvard Univ, Dept Stat, Cambridge, MA 02138 USA Broad Inst MIT & Harvard, Cambridge, MA 02142 USA Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R ChinaWang, Chaolong论文数: 0 引用数: 0 h-index: 0机构: Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Dept Epidemiol & Biostat, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Natl Med Ctr Major Publ Hlth Events, Wuhan, Peoples R China Huazhong Univ Sci & Technol, Tongji Med Coll, Sch Publ Hlth, Minist Educ,Key Lab Environm & Hlth,State Key Lab, Wuhan, Peoples R China
- [10] Dynamics of a fractional order mathematical model for COVID-19 epidemic transmissionPHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2023, 609Arshad, Sadia论文数: 0 引用数: 0 h-index: 0机构: COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, PakistanSiddique, Imran论文数: 0 引用数: 0 h-index: 0机构: Univ Management & Technol, Dept Math, Lahore 54770, Pakistan COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, PakistanNawaz, Fariha论文数: 0 引用数: 0 h-index: 0机构: COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, PakistanShaheen, Aqila论文数: 0 引用数: 0 h-index: 0机构: Minhaj Univ, Sch Math, Lahore, Pakistan COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, PakistanKhurshid, Hina论文数: 0 引用数: 0 h-index: 0机构: Minhaj Univ, Sch Math, Lahore, Pakistan COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan