2012, 9(4): 877-898. doi: 10.3934/mbe.2012.9.877

Differential impact of sickle cell trait on symptomatic and asymptomatic malaria

1. 

Department of Epidemiology, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15261

2. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907

3. 

Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287

Received  January 2012 Revised  May 2012 Published  October 2012

Individuals who carry the sickle cell trait ($S$-gene) have a greatly reduced risk of experiencing symptomatic malaria infections. However, previous studies suggest that the sickle cell trait does not protect against acquiring asymptomatic malaria infections, although the proportion of symptomatic infections is up to $50\%$ in areas where malaria is endemic. To examine the differential impact of the sickle cell trait on symptomatic and asymptomatic malaria, we developed a mathematical model of malaria transmission that incorporates the evolutionary dynamics of $S$-gene frequency. Our model indicates that the fitness of sickle cell trait is likely to increase with the proportion of symptomatic malaria infections. Our model also shows that control efforts aimed at diminishing the burden of symptomatic malaria are not likely to eradicate malaria in endemic areas, due to the increase in the relative prevalence of asymptomatic infection, the reservoir of malaria. Furthermore, when the prevalence of symptomatic malaria is reduced, both the fitness and frequency of the $S$-gene may decrease. In turn, a decreased frequency of the $S$-gene may eventually increase the overall prevalence of both symptomatic and asymptomatic malaria. Therefore, the control of symptomatic malaria might result in evolutionary repercussions, despite short-term epidemiological benefits.
Citation: Eunha Shim, Zhilan Feng, Carlos Castillo-Chavez. Differential impact of sickle cell trait on symptomatic and asymptomatic malaria. Mathematical Biosciences & Engineering, 2012, 9 (4) : 877-898. doi: 10.3934/mbe.2012.9.877
References:
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M. Aidoo, D. J. Terlouw, M. S. Kolczak, P. D. McElroy, F. O. ter Kuile, S. Kariuki, B. L. Nahlen, A. A. Lal and V. Udhayakumar, Protective effects of the sickle cell gene against malaria morbidity and mortality,, Lancet, 359 (2002), 1311.  doi: 10.1016/S0140-6736(02)08273-9.  Google Scholar

[2]

S. J. Allen, S. Bennett, E. M. Riley, P. A. Rowe, P. H. Jakobsen, A. O'Donnell and B. M. Greenwood, Morbidity from malaria and immune responses to defined Plasmodium. falciparum antigens in children with sickle cell trait in The Gambia,, Trans R Soc Trop Med Hyg., 86 (1992), 494.  doi: 10.1016/0035-9203(92)90083-O.  Google Scholar

[3]

A. C. Allison, Two lessons from the interface of genetics and medicine,, Genetics, 166 (2004), 1591.  doi: 10.1534/genetics.166.4.1591.  Google Scholar

[4]

Z. Y. Aliyu, G. J. Kato, J. 6th Taylor, A. Babadoko, A. I. Mamman, V. R. Gordeuk and M. T. Gladwin, Sickle cell disease and pulmonary hypertension in Africa: A global perspective and review of epidemiology, pathophysiology, and management,, Am J Hematol., 83 (2008), 63.  doi: 10.1002/ajh.21057.  Google Scholar

[5]

L. M. Arriola and J. M. Hyman, Being sensitive to uncertainty,, Science and Engineering, 9 (2007), 10.   Google Scholar

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O. J. Briët, P. Vounatsou, D. M. Gunawardena, G. N. Galappaththy and P. H. Amerasinghe, Temporal correlation between malaria and rainfall in Sri Lanka,, Malar J., 7 (2008).   Google Scholar

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R. Carter and K. N. Mendis, Evolutionary and historical aspects of the burden of malaria,, Clin Microbiol Rev., 15 (2002), 564.  doi: 10.1128/CMR.15.4.564-594.2002.  Google Scholar

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L. F. Chaves, A. Kaneko and M. Pascual, Random, top-down, or bottom-up coexistence of parasites: malaria population dynamics in multi-parasitic settings,, Ecology, 90 (2009), 2414.  doi: 10.1890/08-1022.1.  Google Scholar

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C. Chiyaka, W. Garira and S. Dube, Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas,, Theor Popul Biol., 75 (2009), 14.  doi: 10.1016/j.tpb.2008.10.002.  Google Scholar

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J. R. Coura, M. Suez-Mutis and S. Ladeia-Andrade, A new challenge for malaria control in Brazil: asymptomatic Plasmodium infection-a review,, Mem. Inst. Oswaldo Cruz., 101 (2006), 229.  doi: 10.1590/S0074-02762006000300001.  Google Scholar

[11]

M. Creary, D. Williamson and R. Kulkarni, Sickle cell disease: current activities, public health implications, and future directions,, Journal of Women's Health, 16 (2007), 575.  doi: 10.1089/jwh.2007.CDC4.  Google Scholar

[12]

T. Day, Insights from Price's equation into evolutionary epidemiology,, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 71 (2006), 23.   Google Scholar

[13]

N. Dhingra, P. Jha, V. P. Sharma, A. A. Cohen, R. M. Jotkar, P. S. Rodriguez, D. G. Bassani, W. Suraweera, R. Laxminarayan, R. Peto and Million Death Study Collaborators, Adult and child malaria mortality in India: a nationally representative mortality survey,, Lancet, 376 (2010), 1768.  doi: 10.1016/S0140-6736(10)60831-8.  Google Scholar

[14]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population,, J. Math. Biol., 28 (1990).  doi: 10.1007/BF00178324.  Google Scholar

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Z. Feng and C. Castillo-Chavez, The influence of infectious disease on population genetics,, Mathemtical Biosciences and Engineering, 3 (2006), 467.   Google Scholar

[16]

Z. Feng, D. L. Smith, F. E. McKenzie and S. A. Levin, Coupling ecology and evolution: malaria and the S-gene across time scales,, Math. Biosci., 189 (2004), 1.  doi: 10.1016/j.mbs.2004.01.005.  Google Scholar

[17]

Z. Feng, Y. Yi and H. Zhu, Fast and slow dynamics of malaria and the S-gene frequency,, Journal of Dynamics and Differential Equations, 16 (2004), 869.  doi: 10.1007/s10884-004-7828-6.  Google Scholar

[18]

J. A. Filipe, E. M. Riley, C. J. Drakeley, C. J. Sutherland and A. C. Ghani, Determination of the processes driving the acquisition of immunity to malaria using a mathematical transmission model,, PLoS Comput Biol., 3 (2007).   Google Scholar

[19]

W. Gu, C. M. Mbogo, J. I. Githure, J. L. Regens, G. F. Killeen, C. M. Swalm, G. Yan and J. C. Beier, Low recovery rates stabilize malaria endemicity in areas of low transmission in coastal Kenya,, Acta Tropica, 86 (2003), 71.  doi: 10.1016/S0001-706X(03)00020-2.  Google Scholar

[20]

M. Harada, T. Ikeshoji and S. Suguri, Studies on vector control by osquito Candle,, in, (1988), 120.   Google Scholar

[21]

H. Ishikawa, A. Ishii, N. Nagai, H. Ohmae, M. Harada, S. Suguri and J. Leafasia, A mathematical model for the transmission of Plasmodium vivax malaria,, Parasitol. Int., 52 (2003), 81.  doi: 10.1016/S1383-5769(02)00084-3.  Google Scholar

[22]

T. R. Jones, Quantitative aspects of the relationship between the sickle-cell gene and malaria,, Parasitol. Today, 13 (1997).  doi: 10.1016/S0169-4758(96)10083-1.  Google Scholar

[23]

A. Kaneko, A community-directed strategy for sustainable malaria elimination on islands: short-term MDA integrated with ITNs and robust surveillance,, Acta Trop., 114 (2010), 177.  doi: 10.1016/j.actatropica.2010.01.012.  Google Scholar

[24]

A. Kaneko, G. Taleo, M. Kalkoa, J. Yaviong, P. A. Reeve, M. Ganczakowski, C. Shirakawa, K. Palmer, T. Kobayakawa and A. Björkman, Malaria epidemiology, glucose 6-phosphate dehydrogenase deficiency and human settlement in the Vanuatu Archipelago,, Acta Trop., 70 (1998), 285.  doi: 10.1016/S0001-706X(98)00035-7.  Google Scholar

[25]

S. E. Kern, A. B. Tiono, M. Makanga, A. D. Gbadoe, Z. Premji, O. Gaye, I. Sagara, D. Ubben, M. Cousin, F. Oladiran, O. Sander and B. Ogutu, Community screening and treatment of asymptomatic carriers of Plasmodium falciparum with artemether-lumefantrine to reduce malaria disease burden: A modelling and simulation analysis,, Malar J., 10 (2011).   Google Scholar

[26]

D. P. Kwiatkowski, How malaria has affected the human genome and what human genetics can teach us about malaria,, Am J. Hum Genet., 77 (2005), 171.  doi: 10.1086/432519.  Google Scholar

[27]

S. Males, O. Gaye and A. Garcia, Long-term asymptomatic carriage of Plasmodium falciparum protects from malaria attacks: A prospective study among Senegalese children,, Clin Infect Dis., 46 (2008), 516.   Google Scholar

[28]

S. L. Nsobya, S. Parikh, F. Kironde, G. Lubega, M. R. Kamya, P. J. Rosenthal and G. Dorsey, Molecular evaluation of the natural history of asymptomatic parasitemia in Ugandan children,, J Infect Dis., 189 (2004), 2220.  doi: 10.1086/421281.  Google Scholar

[29]

L. C. Okell, C. J. Drakeley, A. C. Ghani, T. Bousema and C. J. Sutherland, Reduction of transmission from malaria patients by artemisinin combination therapies: a pooled analysis of six randomized trials,, Malar J, 7 (2008).   Google Scholar

[30]

L. C. Okell, J. T. Griffin, I. Kleinschmidt, T. D. Hollingsworth, T. S. Churcher, M. J. White, T. Bousema, C. J. Drakeley and A. C. Ghani, The potential contribution of mass treatment to the control of Plasmodium falciparum malaria,, PLoS One, 6 (2011).   Google Scholar

[31]

P. Olliaro, J. Cattani and D. Wirth, Malaria, the submerged disease,, JAMA, 275 (1996), 230.  doi: 10.1001/jama.275.3.230.  Google Scholar

[32]

W. Pongtavornpinyo, S. Yeung, I. M. Hastings, A. M. Dondorp, N. P. Day and N. J. White, Spread of anti-malarial drug resistance: mathematical model with implications for ACT drug policies,, Malar J., 7 (2008).   Google Scholar

[33]

R. Ross, "The Prevention of Malaria,", John Murray, (1911).   Google Scholar

[34]

S. Ruan, D. Xiao and J. C. Beier, On the delayed ross-macdonald model for malaria transmission,, Bulletin of Mathematical Biology, 70 (2008), 1098.  doi: 10.1007/s11538-007-9292-z.  Google Scholar

[35]

B. Singh, S. L. Kim, A. Matusop, A. Radhakrishnan, S. S. Shamsul, J. Cox-Singh, J., et al., A large focus of naturally acquired Plasmodium knowlesi infections in human beings,, Lancet, 363 (2004), 1017.   Google Scholar

[36]

M. Vafa, M. Troye-Blomberg, J. Anchang, A. Garcia and F. Migot-Nabias, Multiplicity of Plasmodium falciparum infection in asymptomatic children in Senegal: relation to transmission, age and erythrocyte variants,, Malaria J., 7 (2008).   Google Scholar

[37]

M. Van Veelen, On the use of the Price equation,, Journal of Theoretical Biology, 237 (2005), 412.  doi: 10.1016/j.jtbi.2005.04.026.  Google Scholar

[38]

T. N. Williams, Human red blood cell polymorphisms and malaria,, Curr Opin Microbiol., 9 (2006), 388.   Google Scholar

[39]

S. Yeung, W. Pongtavornpinyo, I. M. Hastings, A. J. Mills and N. J. White, Antimalarial drug resistance, artemisinin-based combination therapy, and the contribution of modelling to elucidating policy choices,, Am. J. Trop. Med. Hyg., 71 (2004), 179.   Google Scholar

[40]

Centers for Disease Control and Prevention., The history of Malaria, an ancient disease,, , ().   Google Scholar

[41]

Time Healthland, Drug-Resistant malaria is spreading, and it could be a public health disaster,, , ().   Google Scholar

[42]

, , http://web.worldbank.org/WBSITE/EXTERNAL/COUNTRIES/AFRICAEXT/ 0, ().   Google Scholar

[43]

World Health Organization, Fifty-eighth World Health Assembly, Report by the Secretariat., Malaria,, , ().   Google Scholar

show all references

References:
[1]

M. Aidoo, D. J. Terlouw, M. S. Kolczak, P. D. McElroy, F. O. ter Kuile, S. Kariuki, B. L. Nahlen, A. A. Lal and V. Udhayakumar, Protective effects of the sickle cell gene against malaria morbidity and mortality,, Lancet, 359 (2002), 1311.  doi: 10.1016/S0140-6736(02)08273-9.  Google Scholar

[2]

S. J. Allen, S. Bennett, E. M. Riley, P. A. Rowe, P. H. Jakobsen, A. O'Donnell and B. M. Greenwood, Morbidity from malaria and immune responses to defined Plasmodium. falciparum antigens in children with sickle cell trait in The Gambia,, Trans R Soc Trop Med Hyg., 86 (1992), 494.  doi: 10.1016/0035-9203(92)90083-O.  Google Scholar

[3]

A. C. Allison, Two lessons from the interface of genetics and medicine,, Genetics, 166 (2004), 1591.  doi: 10.1534/genetics.166.4.1591.  Google Scholar

[4]

Z. Y. Aliyu, G. J. Kato, J. 6th Taylor, A. Babadoko, A. I. Mamman, V. R. Gordeuk and M. T. Gladwin, Sickle cell disease and pulmonary hypertension in Africa: A global perspective and review of epidemiology, pathophysiology, and management,, Am J Hematol., 83 (2008), 63.  doi: 10.1002/ajh.21057.  Google Scholar

[5]

L. M. Arriola and J. M. Hyman, Being sensitive to uncertainty,, Science and Engineering, 9 (2007), 10.   Google Scholar

[6]

O. J. Briët, P. Vounatsou, D. M. Gunawardena, G. N. Galappaththy and P. H. Amerasinghe, Temporal correlation between malaria and rainfall in Sri Lanka,, Malar J., 7 (2008).   Google Scholar

[7]

R. Carter and K. N. Mendis, Evolutionary and historical aspects of the burden of malaria,, Clin Microbiol Rev., 15 (2002), 564.  doi: 10.1128/CMR.15.4.564-594.2002.  Google Scholar

[8]

L. F. Chaves, A. Kaneko and M. Pascual, Random, top-down, or bottom-up coexistence of parasites: malaria population dynamics in multi-parasitic settings,, Ecology, 90 (2009), 2414.  doi: 10.1890/08-1022.1.  Google Scholar

[9]

C. Chiyaka, W. Garira and S. Dube, Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas,, Theor Popul Biol., 75 (2009), 14.  doi: 10.1016/j.tpb.2008.10.002.  Google Scholar

[10]

J. R. Coura, M. Suez-Mutis and S. Ladeia-Andrade, A new challenge for malaria control in Brazil: asymptomatic Plasmodium infection-a review,, Mem. Inst. Oswaldo Cruz., 101 (2006), 229.  doi: 10.1590/S0074-02762006000300001.  Google Scholar

[11]

M. Creary, D. Williamson and R. Kulkarni, Sickle cell disease: current activities, public health implications, and future directions,, Journal of Women's Health, 16 (2007), 575.  doi: 10.1089/jwh.2007.CDC4.  Google Scholar

[12]

T. Day, Insights from Price's equation into evolutionary epidemiology,, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 71 (2006), 23.   Google Scholar

[13]

N. Dhingra, P. Jha, V. P. Sharma, A. A. Cohen, R. M. Jotkar, P. S. Rodriguez, D. G. Bassani, W. Suraweera, R. Laxminarayan, R. Peto and Million Death Study Collaborators, Adult and child malaria mortality in India: a nationally representative mortality survey,, Lancet, 376 (2010), 1768.  doi: 10.1016/S0140-6736(10)60831-8.  Google Scholar

[14]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population,, J. Math. Biol., 28 (1990).  doi: 10.1007/BF00178324.  Google Scholar

[15]

Z. Feng and C. Castillo-Chavez, The influence of infectious disease on population genetics,, Mathemtical Biosciences and Engineering, 3 (2006), 467.   Google Scholar

[16]

Z. Feng, D. L. Smith, F. E. McKenzie and S. A. Levin, Coupling ecology and evolution: malaria and the S-gene across time scales,, Math. Biosci., 189 (2004), 1.  doi: 10.1016/j.mbs.2004.01.005.  Google Scholar

[17]

Z. Feng, Y. Yi and H. Zhu, Fast and slow dynamics of malaria and the S-gene frequency,, Journal of Dynamics and Differential Equations, 16 (2004), 869.  doi: 10.1007/s10884-004-7828-6.  Google Scholar

[18]

J. A. Filipe, E. M. Riley, C. J. Drakeley, C. J. Sutherland and A. C. Ghani, Determination of the processes driving the acquisition of immunity to malaria using a mathematical transmission model,, PLoS Comput Biol., 3 (2007).   Google Scholar

[19]

W. Gu, C. M. Mbogo, J. I. Githure, J. L. Regens, G. F. Killeen, C. M. Swalm, G. Yan and J. C. Beier, Low recovery rates stabilize malaria endemicity in areas of low transmission in coastal Kenya,, Acta Tropica, 86 (2003), 71.  doi: 10.1016/S0001-706X(03)00020-2.  Google Scholar

[20]

M. Harada, T. Ikeshoji and S. Suguri, Studies on vector control by osquito Candle,, in, (1988), 120.   Google Scholar

[21]

H. Ishikawa, A. Ishii, N. Nagai, H. Ohmae, M. Harada, S. Suguri and J. Leafasia, A mathematical model for the transmission of Plasmodium vivax malaria,, Parasitol. Int., 52 (2003), 81.  doi: 10.1016/S1383-5769(02)00084-3.  Google Scholar

[22]

T. R. Jones, Quantitative aspects of the relationship between the sickle-cell gene and malaria,, Parasitol. Today, 13 (1997).  doi: 10.1016/S0169-4758(96)10083-1.  Google Scholar

[23]

A. Kaneko, A community-directed strategy for sustainable malaria elimination on islands: short-term MDA integrated with ITNs and robust surveillance,, Acta Trop., 114 (2010), 177.  doi: 10.1016/j.actatropica.2010.01.012.  Google Scholar

[24]

A. Kaneko, G. Taleo, M. Kalkoa, J. Yaviong, P. A. Reeve, M. Ganczakowski, C. Shirakawa, K. Palmer, T. Kobayakawa and A. Björkman, Malaria epidemiology, glucose 6-phosphate dehydrogenase deficiency and human settlement in the Vanuatu Archipelago,, Acta Trop., 70 (1998), 285.  doi: 10.1016/S0001-706X(98)00035-7.  Google Scholar

[25]

S. E. Kern, A. B. Tiono, M. Makanga, A. D. Gbadoe, Z. Premji, O. Gaye, I. Sagara, D. Ubben, M. Cousin, F. Oladiran, O. Sander and B. Ogutu, Community screening and treatment of asymptomatic carriers of Plasmodium falciparum with artemether-lumefantrine to reduce malaria disease burden: A modelling and simulation analysis,, Malar J., 10 (2011).   Google Scholar

[26]

D. P. Kwiatkowski, How malaria has affected the human genome and what human genetics can teach us about malaria,, Am J. Hum Genet., 77 (2005), 171.  doi: 10.1086/432519.  Google Scholar

[27]

S. Males, O. Gaye and A. Garcia, Long-term asymptomatic carriage of Plasmodium falciparum protects from malaria attacks: A prospective study among Senegalese children,, Clin Infect Dis., 46 (2008), 516.   Google Scholar

[28]

S. L. Nsobya, S. Parikh, F. Kironde, G. Lubega, M. R. Kamya, P. J. Rosenthal and G. Dorsey, Molecular evaluation of the natural history of asymptomatic parasitemia in Ugandan children,, J Infect Dis., 189 (2004), 2220.  doi: 10.1086/421281.  Google Scholar

[29]

L. C. Okell, C. J. Drakeley, A. C. Ghani, T. Bousema and C. J. Sutherland, Reduction of transmission from malaria patients by artemisinin combination therapies: a pooled analysis of six randomized trials,, Malar J, 7 (2008).   Google Scholar

[30]

L. C. Okell, J. T. Griffin, I. Kleinschmidt, T. D. Hollingsworth, T. S. Churcher, M. J. White, T. Bousema, C. J. Drakeley and A. C. Ghani, The potential contribution of mass treatment to the control of Plasmodium falciparum malaria,, PLoS One, 6 (2011).   Google Scholar

[31]

P. Olliaro, J. Cattani and D. Wirth, Malaria, the submerged disease,, JAMA, 275 (1996), 230.  doi: 10.1001/jama.275.3.230.  Google Scholar

[32]

W. Pongtavornpinyo, S. Yeung, I. M. Hastings, A. M. Dondorp, N. P. Day and N. J. White, Spread of anti-malarial drug resistance: mathematical model with implications for ACT drug policies,, Malar J., 7 (2008).   Google Scholar

[33]

R. Ross, "The Prevention of Malaria,", John Murray, (1911).   Google Scholar

[34]

S. Ruan, D. Xiao and J. C. Beier, On the delayed ross-macdonald model for malaria transmission,, Bulletin of Mathematical Biology, 70 (2008), 1098.  doi: 10.1007/s11538-007-9292-z.  Google Scholar

[35]

B. Singh, S. L. Kim, A. Matusop, A. Radhakrishnan, S. S. Shamsul, J. Cox-Singh, J., et al., A large focus of naturally acquired Plasmodium knowlesi infections in human beings,, Lancet, 363 (2004), 1017.   Google Scholar

[36]

M. Vafa, M. Troye-Blomberg, J. Anchang, A. Garcia and F. Migot-Nabias, Multiplicity of Plasmodium falciparum infection in asymptomatic children in Senegal: relation to transmission, age and erythrocyte variants,, Malaria J., 7 (2008).   Google Scholar

[37]

M. Van Veelen, On the use of the Price equation,, Journal of Theoretical Biology, 237 (2005), 412.  doi: 10.1016/j.jtbi.2005.04.026.  Google Scholar

[38]

T. N. Williams, Human red blood cell polymorphisms and malaria,, Curr Opin Microbiol., 9 (2006), 388.   Google Scholar

[39]

S. Yeung, W. Pongtavornpinyo, I. M. Hastings, A. J. Mills and N. J. White, Antimalarial drug resistance, artemisinin-based combination therapy, and the contribution of modelling to elucidating policy choices,, Am. J. Trop. Med. Hyg., 71 (2004), 179.   Google Scholar

[40]

Centers for Disease Control and Prevention., The history of Malaria, an ancient disease,, , ().   Google Scholar

[41]

Time Healthland, Drug-Resistant malaria is spreading, and it could be a public health disaster,, , ().   Google Scholar

[42]

, , http://web.worldbank.org/WBSITE/EXTERNAL/COUNTRIES/AFRICAEXT/ 0, ().   Google Scholar

[43]

World Health Organization, Fifty-eighth World Health Assembly, Report by the Secretariat., Malaria,, , ().   Google Scholar

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