Research article

Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis

  • Received: 12 September 2018 Accepted: 10 June 2019 Published: 09 August 2019
  • In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.

    Citation: Sarah Treibert, Helmut Brunner, Matthias Ehrhardt. Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7250-7298. doi: 10.3934/mbe.2019364

    Related Papers:

  • In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.


    加载中


    [1] B. Brodhun, D. Altman, B. Hauer, et al., Bericht zur Epidemiologie der Tuberkulose in Deutschland für 2017 (Report on the epidemiology of tuberculosis in Germany for 2017) (in german), Robert Koch-Institut, Berlin 2018.
    [2] K. Bozorgmehr, C. Stock, B. Joggerst, et al., Tuberculosis screening in asylum seekers in Germany: a need for better data, The Lancet, 3 (2018), Pe359–e361.
    [3] K. Bozorgmehr, S. Preussler, U. Wagner, et al., Using country of origin to inform targeted tuberculosis screening in asylum seekers: a modelling study of screening data in a German federal state, 2002-2015, BMC Infect. Diseases, 19 (2019), 304.
    [4] R. Diel, S. Rüsch-Gerdes and S. Niemann, Molecular Epidemiology of Tuberculosis among Immigrants in Hamburg, Germany, J. Clin. Microbiol., 42 (2004), 2952–2960.
    [5] H. Guoand J. Wu, Persistenthigh incidence of tuberculosisamong immigrants in alow-incidence country: impact of immigrants with early or late latency, Math. Biosci. Eng., 8 (2011), 695–709.
    [6] J. Zhang, Y. Li and X. Zhang, Mathematical modeling of tuberculosis data of China, J. Theor. Biol., 365 (2015), 159–163.
    [7] Focus, Tuberkulosefälle in Deutschland nehmen wieder zu – vor allem in den Großstädten (Tuberculosis cases in Germany on the rise again – especially in large cities) (in german), March 23, 2017,
    [8] R. W. Aldridge, D. Zenner, P. J. White, et al., Tuberculosis in migrants moving from high-incidence to low-incidence countries: a population-based cohort study of 519 955 migrants screened before entry to England, Wales, and Northern Ireland, The Lancet, October 11, 2016.
    [9] N. A. Menzies, A. N. Hill, T. Cohen, et al., The impact of migration on tuberculosis in the United States, Int. J. Tuberc. Lung Dis., 22 (2018), 1392–1403.
    [10] D. P. Moualeu, S. Röblitz, R. Ehrig, et al., Parameter Identification for a Tuberculosis Model in Cameroon, PLoS ONE, 10 (2015), e0120607.
    [11] D. P. Moualeu, A. N. Yakam, S. Bowong, et al., Analysis of a tuberculosis model with undetected and lost-sight cases, Commun. Nonlin. Sci. Numer. Simul., 41 (2016), 48–63.
    [12] M. Pareek, C. Greenaway, T. Noori, et al., The impact of migration on tuberculosis epidemiology and control in high-income countries: a review, BMC Med., 14 (2016), 48.
    [13] R. P. Sigdel and C. C. McCluskey, Global stability for an SEI model of infectious disease with immigration, Appl. Math. Comput., 243 (2014), 684–689.
    [14] Z. White, J. Painter, P. Douglas, et al., Immigrant Arrival and Tuberculosis among Large Immigrant- and Refugee-Receiving Countries, 2005–2009, Tuberc. Res. Treat., 2017 (2017), Article 8567893.
    [15] Y. Zhou and H. Cao, Discrete tuberculosis models and their application, in: S. Sivaloganathan (ed.), New Perspectives in Mathematical Biology, Fields Institute Communications 57, 2010.
    [16] R. Loddenkemper, J. F. Murray, C. Gradmann, et al., History of tuberculosis, Chapter 2 in: G.B. Migliori, G. Bothamley, R. Duarte, A. Rendon (eds.) Tuberculosis, ERS Monograph 82, 2018.
    [17] N. E. Aronson, M. Santosham, G. W. Comstock, et al., Long-term efficacy of BCG vaccine in American indians and Alaska natives, JAMA, 291 (2004), 2086–2091.
    [18] J. P. Higgins, K. Soares-Weiser, J. A. Lopez-Lopez, et al., Association of BCG, DTP, and measles containing vaccines with childhood mortality: systematic review, BMJ, 355 (2016), i5170.
    [19] P. Aaby, T. R. Kollmann and C. S. Benn, Nonspecific effects of neonatal and infant vaccination: public-health, immunological and conceptual challenges, Nat. Immunol., 15 (2014), 895–899.
    [20] S. Biering-Sørensen, K. J. Jensen, I. Monterio, et al., Rapid protective effects of early BCG on neonatal mortality among low birth weight boys: Observations from randomized trials, J. Infect. Dis., 217 (2018), 759–766.
    [21] V. Nankabirwa, J. K. Tumwine, O. Namugga, et al., Early versus late BCG vaccination in HIV-1-exposed infants in Uganda: study protocol for a randomized controlled trial, Trials, 18 (2017), 152–169.
    [22] M. G. Netea, L. A. Joosten, E. Latz, et al., Trained immunity: A program of innate immune memory in health and disease, Science, 352 (2016), aaf1098.
    [23] M. G. Netea, J. Quintin and J. van der Meer, Trained Immunity: A memory for innate host defense, Cell Press, Cell Host and Microbe, 2011.
    [24] M. G. Netea, Training innate immunity: The changing concept of immunological memory in innate host defence, Eur. J. Clin. Invest., 43 (2013), 881–884.
    [25] F. Shann, The non-specific effects of vaccines, Arch. Dis. Child., 95 (2010), 662–667.
    [26] C. B. Wilson, Applying contemporary immunology to elucidate heterologous effects of infant vaccines and to better inform maternal-infant immunization practices, Front. Immunol., 6 (2015), 64.
    [27] WHO, Global tuberculosis report 2017.
    [28] European Centre for Disease Prevention and Control/WHO Regional Office for Europe, Tuberculosis surveillance and monitoring in Europe 2017.
    [29] K. Lönnroth, G. B. Migliori, I. Abubakar, et al., Towards tuberculosis elimination: an action framework for low-incidence countries, Eur. Respir. J., 45 (2015), 928–952.
    [30] RKI, Berichte zur Epidemiologie der Tuberkulose in Deutschland für 2016 (Reports on the epidemiology of tuberculosis in Germany for 2016).
    [31] B. Hauer and N. Perumal, Tuberkulose bleibt eine Herausforderung auch für Deutschland (Tuberculosis remains a challenge for Germany as well) (in german), Epid. Bull., 11/12 (2018), 109–111.
    [32] N. T. Mutters, F. Günther, A. Sander, et al., Influx of multidrug-resistant organisms by country-to-country transfer of patients, BMC Infect. Diseases, 15 (2015), 466–472.
    [33] A. Roy, M. Eisenhut, R. J. Harris, et al., Effect of BCG vaccination against Mycobacterium tuberculosis infection in children: systematic review and meta-analysis, BMJ, 349 (2014), g4643.
    [34] C. A. Thaissa and S. H. E. Kaufmann, Toward novel vaccines against tuberculosis: Current hopes and obstacles, Yale J. Biol. Med., 83 (2010), 209–215.
    [35] B. E. Kwon, J. H. Ahn, S. Min, et al., Development of new preventive and therapeutic vaccines for tuberculosis, Immune. Netw., 18 (2018), e17.
    [36] C. S. Merle, S. S. Cunha and L. C. Rodrigues, BCG vaccination and leprosy protection: review of current evidence and status of BCG in leprosy control, Expert Rev. Vaccines, 9 (2010), 209–222.
    [37] S. Chen, N. Zhang, J. Shao, et al., Maintenance versus non-maintenance intravesical Bacillus Calmette-Guérin instillation for non-muscle invasive bladder cancer: A systematic review and meta-analysis of randomized clinical trials, Int. J. Surg., 52 (2018), 248–257.
    [38] V. Nankabirwa, J. K. Tumwine, P. M. Mugaba, et al., Child survival and BCG vaccination: a community based prospective cohort study in Uganda, BMC Public Health., 15 (2015), 175–185.
    [39] M. G. Netea and R. van Crevel, BCG-induced protection: Effects on innate immune memory, Semin. Immunol., 26 (2014), 512–517.
    [40] B. Freyne, A. Marchant, N. Curtis, et al., BCG-associated heterologous immunity, a historical perspective: experimental models and immunological mechanisms, Trans. R. Soc. Trop. Med. Hyg., 109 (2015), 46–51.
    [41] P. Aaby, A. Roth, H. Ravn, et al., Randomized trial of BCG vaccination at birth to low-birth-weight children: beneficial nonspecific effects in the neonatal period?, J. Infect. Dis., 204 (2011), 245–252.
    [42] R. Kandasamy, M. Voysey, F. McQuaid, et al., Non-specific immunological effects of selected routine childhood immunisations: systematic review, BMJ, 355 (2016), i5225.
    [43] R. Ragonnet, J. Trauer, J. Denholm, et al., Vaccination programs for endemic infections: Modelling real versus apparent impacts of vaccine and infection characteristics, Nature Sci, Rep,, 5 (2015), 15468.
    [44] F. Shann, H. Nohynek, J. A. Scott, et al., Randomized trials to study the nonspecific effects of vaccines in children in low-income countries, Pediatr. Infect. Dis. J., 29 (2010), 457–461.
    [45] S. Sorup, M. Villumsen, H. Ravn, et al., Smallpox vaccination and all-cause infectious disease hospitalization: a Danish register-based cohort study, Int. J. Epidemiol., 40 (2011), 955-963.
    [46] S. Sorup, C. S. Benn, A. Poulsen, et al., Live vaccine against measles, mumps, and rubella and the risk of hospital admissions for nontargeted infections, JAMA, 311 (2014), 826-835.
    [47] WHO, Systematic review of the non-specific immunological effects of selected routine immunizations, Oxford University, 2015.
    [48] L. C. J. de Bree, V. A. C. M. Koeken, L. A. B. Joosten, et al., Non-specific effects of vaccines: Current evidence and potential implications, Semin. Immunol., 39 (2018), 35–43.
    [49] D. Uthayakumar, S. Paris, L. Chapat, et al., Non-specific Effects of Vaccines Illustrated Through the BCG Example: From Observations to Demonstrations, Front. Immunol., 9 (2018), Article 2869.
    [50] C. S. Benn, A. B. Fisker, A. Rieckmann, et al., How to evaluate potential non-specific effects of vaccines: the quest for randomized trials or time for triangulation?, Expert Rev. Vaccines, 17 (2018), 411–420.
    [51] M. J. de Castro, J. Pardo-Seco, F. Martinón-Torres, et al., Nonspecific (heterologous) protection of neonatal BCG vaccination against hospitalization due to respiratory infection and sepsis, Clin. Infect. Dis., 60 (2015), 1611–1619.
    [52] L. Sanders, S. Maiwald and H. Brunner, Epidemiologische Studie zu spezifischen und unspezifischen Wirkungen der BCG-Impfung in Deutschland mit Kosten-Nutzen-Bewertung (Epidemiological study on specific and non-specific effects of BCG vaccination in Germany with cost-benefit assessment) (in german), 62. Annual Conference of the German Society for Medical Informatics, Biometry and Epidemiology, Oldenburg 2017.
    [53] J. Leentjens, M. Kox, R. Stokman, et al., BCG vaccination enhances the immunogenicity of subsequent Influenza vaccination in healthy volunteers: a randomized, placebo-controlled pilot study, J. Infect. Dis., 212 (2015), 1930–1938.
    [54] K. L. Flanagan, S. L. Klein, N. E. Skakkebaek, et al., Sex differences in the vaccine-specific and non-targeted effects of vaccines, Vaccine, 29 (2011), 349–354.
    [55] L. G. Stensballe, S. Sørup, P. Aaby, et al., BCG vaccination at birth and early childhood hospitalisation: a randomised clinical multicentre trial, Arch. Dis. Child., 102 (2017), 224–231.
    [56] L. G. Stensballe, H. Ravn, N. Birk, et al., BCG vaccination at birth and rate of hospitalization for Infection until 15 months of age in Danish children: A randomized clinical multicenter trial, J. Pediatric Infect. Dis. Soc., 2018.
    [57] A. Rieckmann, M. Villumsen, M. L. Jensen, et al., The effect of smallpox and Bacillus Calmette-Guérin vaccination on the risk of Human Immunodeficiency Virus-1 infection in Guinea-Bissau and Denmark, Open Forum Infect. Dis., 4 (2017), ofx 130.
    [58] S. Prentice, E. L. Webb, H. M. Dockrell, et al., Investigating the non-specific effects of BCG vaccination on the innate immune system in Ugandan neonates: study protocol for a randomised controlled trial, Trials, 16 (2015), 149–161.
    [59] C. S. Benn, A. B. Fisker, H. C. Whittle, et al., Revaccination with live attenuated vaccines confer additional beneficial nonspecific effects on overall survival: A review, EBioMedicine, 10 (2016), 312–317.
    [60] N. M. Birk, T. N. Nissen, J. Kjægaard, et al., Effects of Bacillus Calmette-Guérin (BCG) vaccination at birth on T and B lymphocyte subsets: Results from a clinical randomized trial, Sci. Rep., 7 (2017), 12398.
    [61] S. Saeed, J. Quintin, H. H. Kerstens, et al., Epigenetic programming of monocyte-to-macrophage differentiation and trained innate immunity, Science, 345 (2014), 1251086.
    [62] J. Kleinnijenhuis, J. Quntin, F. Preijers, et al., Bacille Calmette-Guérin induces NOD2-dependent nonspecific protection from reinfection via epigenetic reprogramming of monocytes, Proc. Natl. Acad. Sci. USA, 109 (2012), 17537–17542.
    [63] Y. L. Lee, J. Y. Lee, Y. H. Jang, et al., Non-specific effects of vaccines: immediate protection against Respiratory Syncytial Virus infection by Line Attenuated Influenza Vaccine, Front. Microbiol., 9 (2018), Article 83.
    [64] R. J. W. Arts, S. J. C. F. M. Moorlag, B. Novakovic, et al., BCG Vaccination Protects against Experimental Viral Infection in Humans through the Induction of Cytokines Associated with Trained Immunity, Cell Host & Microbe., 23 (2018), 89–100.e5.
    [65] B. Freyne, S. Donath, S. Germano, et al., Neonatal BCG vaccination influences cytokine responses to Toll-like Receptor ligands and heterologous antigens, J. Infect. Dis., 217 (2018), 1798–1808.
    [66] G. A. Weinberg and P. G. Szilagy, Vaccine epidemiology: Efficacy, effectiveness, and the translational research road map, J. Infect. Dis., 201 (2010), 1607–1610.
    [67] M. L. McHugh, The odds ratio: calculation, usage, and interpretation, Biochemica Medica, 19 (2009), 120–126.
    [68] S. Gao, Z. Teng, J. Nieto, et al., Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay, J. Biomed. Biotechnol., 2007 (2007), 64870.
    [69] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361–404.
    [70] C. Ozcaglar, A Shabbear, S. L. Vandenberg, et al., Epidemiological models of Mycobacterium tuberculosis complex infections, Math. Biosci., 236 (2012), 77-9-6.
    [71] V. P. Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
    [72] WHO, Surveillance Report, 2012–2017, available from: https://ecdc.europa.eu/sites/portal/files/media/en/publications/Publications/ecdc-tuberculosis-surveillance-monitoring-Europe-2017.pdf
    [73] WHO, Vaccine-preventable diseases: monitoring system 2018 global summary, available from: http://apps.who.int/immunization_monitoring/globalsummary/timeseries/ tswucoveragebcg.html
    [74] K. Styblo and J. Meijer, Impact of BCG vaccination programmes in children and young adults on the tuberculosis problem, Tubercle, 57 (1976), 17–43.
    [75] J. Kleinnijenhuis, J. Quintin, F. Preijers, et al., Long-Lasting Effects of BCG Vaccination on Both Heterologous Th1/Th17 Responses and Innate Trained Immunity, J. Innate. Immun., 6 (2014), 152–158.
    [76] Health Data, South Sudan, available from: http://www.healthdata.org/south-sudan
    [77] Health Data, Guinea-Bissau, available from: http://www.healthdata.org/guinea-bissau
    [78] Index Mundi, Country Comparison: Guinea-Bissau vs. South Sudan, available from: http: //www.indexmundi.com/factbook/compare/guinea-bissau.south-sudan
    [79] WHO, Vaccine-preventable diseases: monitoring system 2018 global summary, Guinea Bissau, available from: http://apps.who.int/immunization_monitoring/globalsummary/estimates?c=GNB
    [80] WHO, Vaccine-preventable diseases: monitoring system 2018 global summary, South Sudan, available from: http://apps.who.int/immunization_monitoring/globalsummary/coverages?c=SSD
    [81] UN, available from: http://www.childmortality.org/files_v20/download/IGME% 20Report%202015_9_3%20LR%20Web.pdf (Inter-agency Group for Child Mortality Estimation, 2010–2015)
    [82] UNICEF, available from: http://data.unicef.org/resources/state-worlds-children-2016-statistical-tables/ (2007–2016)
    [83] P. Mangtani, P. Nguipdop-Djomo, R. H. Keogh, et al., The duration of protection of school-aged BCG vaccination in England: a population-based case–control study, Int. J. Epidemiol., 47 (2017), 193–201.
    [84] D. P. Gao and N. J. Huang, A note on global stability for a tuberculosis model, Appl. Math. Lett., 73 (2017), 163–168.
    [85] D. P. Gao and N. J. Huang, Optimal control analysis of a tuberculosis model, Appl. Math. Modell., 58 (2018), 47–64.
    [86] H.-F. Huo, S.-J. Dang and Y.-N. Li, Stability of a two-strain tuberculosis model with general contact rate, Abstr. Appl. Anal., 2010 (2010), Article ID 293747.
    [87] H.-F. Huo and L.-X. Feng, Global Stability of an Epidemic Model with Incomplete Treatment and Vaccination, Discrete Dyn. Nat. Soc., 2012, Article ID 530267.
    [88] J. Liu and T. Zhang, Global stability for a tuberculosis model, Math. Comput. Modell., 54 (2011), 836–845.
    [89] C. Vargas-De-Leon, On the global stability of infectious diseases models with relapse, Abstraction & Application, 9 (2013), 50–61.
    [90] W. Wojtak, C. J. Silva and D. F. M. Torres, Uniform asymptotic stability of a fractional tuberculosis model, Math. Modell. Natur. Phenom., 13 (2018).
    [91] R. Chinnathambi, F. A. Rihan and H. J. Alsakaji, A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections, Math. Meth. Appl. Sci., May 2019.
    [92] S. Bowong and A. M. A. Alaoui, Optimal intervention strategies for tuberculosis, Commun. Nonlin. Sci. Numer. Simul., 18 (2013), 1441–1453.
    [93] L. J. S. Allen, An Introduction to Stochastic Epidemic Models, in: F. Brauer, P. van den Driessche, J. Wu (eds.), Mathematical Epidemiology. Lecture Notes in Mathematics 1945, Springer, Berlin, Heidelberg, pp 81–130.
    [94] J. L. Dimi and T. Mbaya, Dynamics analysis of stochastic tuberculosis model transmission with immune response, AIMS Math., 3 (2018), 391–408.
    [95] A. El Myr, A. Assadouq, L. Omari, et al., A Stochastic SIR Epidemic System with a Nonlinear Relapse, Discrete Dyn. Nat. Soc., 2018 (2018), Article ID 5493270.
    [96] T. Feng and Y. Qiu, Global analysis of a stochastic TB model with vaccination and treatment, Discrete & Cont. Dyn-B, 24 (2019), 2923–2939.
    [97] Q. Liu, D. Jiang, T. Hayat, et al., Dynamics of a stochastic tuberculosis model with antibiotic resistance, Chaos Solitons & Fract., 109 (2018), 223–230.
    [98] Q. Liu and D. Jiang, The dynamics of a stochastic vaccinated tuberculosis model with treatment, Physica A, 527 (2019), 121274.
    [99] M. Mbokoma and S. C. O. Noutchie, Mathematical analysis of a stochastic tuberculosis model, J. Anal. Appl., 15 (2017), 21–50.
    [100] B. Song, C. Castillo-Chavez andJ. P. Aparicio, Tuberculosis models withfast and slowdynamics: The role of close and casual contacts, Math. Biosci., 180 (2002), 187–205.
    [101] D. Bichara and A. Iggidr, Multi-patch and multi-group epidemic models: a new framework, J. Math. Biol., 77 (2018), 107–134.
    [102] E. Pienaar, A. M. Fluitt, S. E. Whitney, et al., A model of tuberculosis transmission and intervention strategies in an urban residential area, Comput. Biol. Chem., 34 (2010), 86–96.
    [103] X. Hu, Threshold dynamics for a Tuberculosis model with seasonality, Math. Biosci. Eng., 9 (2012), 111–122.
    [104] L. Liu, X.-Q. Zhao and Y. Zhou, A Tuberculosis Model with Seasonality, Bull. Math. Biol., 72 (2010), 931–952.
    [105] H.Xiang, M.-X.ZouandH.-F.Huo, ModelingtheEffectsofHealthEducationandEarlyTherapy on Tuberculosis Transmission Dynamics, Int. J. Nonlin. Sci. Numer. Simul., March 2019.
    [106] N. Blaser, C. Zahnda, S. Hermans, et al., Tuberculosis in Cape Town: An age-structured transmission model, Epidemics, 14 (2016), 54–61.
    [107] R. Xu, Global dynamics of an epidemiological model with age of infection and disease relapse, J. Biol. Dynam., 12 (2017), 118–145.
    [108] L. Liu, X. Ren and Z. Jin, Threshold dynamical analysis on a class of age-structured tuberculosis model with immigration of population, Adv. Diff. Eqs., 2017 (2017), 258.
    [109] S. Khajanchi, D. K. Das and T. K. Kar, Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation, Physica A, 497 (2018), 52–71.
    [110] B. K. Mishra and J. Srivastava, Mathematical model on pulmonary and multidrug-resistant tuberculosis patients with vaccination, J. Egypt. Math. Soc., 22 (2014), 311–316.
    [111] H.-F. Huo and M.-X. Zou, Modelling effects of treatment at home on tuberculosis transmission dynamics, Appl. Math. Modell., 40 (2016), 9474–9484.
    [112] M. J. Keeling and K. T. D. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), 295–307.
    [113] M. E. J. Newman, Spread of epidemic disease on networks, Phys. Rev. E, 66 (2002), 016128.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4724) PDF downloads(697) Cited by(7)

Article outline

Figures and Tables

Figures(7)  /  Tables(16)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog