Mathematical Models & Theory for Malaria

A Bibliography

This is a structured, annotated, chronological bibliography focused on mathematical models for malaria. We wanted an intellectual history of mathematical models for malaria that covered major developments. The bibliography is not intended to be comprehensive.

Also see:

1905-1912

The Prevention of Malaria

In 1897, Ronald Ross identified malaria parasites in the mosquito mid gut [1], securing himself a place in history. Starting around 1899, he turned his attention to the prevention of malaria.

1905

Ross’s interest in mosquito movement is probably an outcome of a debate in 1904 in the British Medical Journal. In 1902, Ross had published Mosquito Brigades and How to Organize Them [2]. The debate was about an attempt at larval source management at a British military base in Myanmar [3].

Ross R | The logical basis of the sanitary policy of mosquito reduction [4]

  • The mathematical model described mosquito movement using the concept of diffusion.

1908

In 1908, Ronald Ross published the first mathematical model describing mosquito-borne pathogen transmission as a system of difference equations.

  • Ross R | Report on the Prevention of Malaria in Mauritius [5].

1910

In 1910, H. Waite was given the unenviable task of checking Ross’s 1908 model.

  • Waite H | Mosquitoes and malaria. A study of the relation between the number of mosquitoes in a locality and the malaria rate [6].

The Prevention of Malaria (1911)

Ross published the second mathematical model of malaria transmission dynamics as a system of differential equations. The model can be found in two places

The Prevention of Malaria (\(2^{nd}\) ed.), by Ross [7]. Note that the model is missing from the \(1^{st}\) edition.

1911

Ross R | Some quantitative studies in epidemiology [8].

1912

Lotka AJ | Quantitative studies in epidemiology [9].

1915-1922

A priori Pathometry (1905-1911)

is a three-part series. Ross started with a solo piece in 1916, but he was joined by Hilda Hudson for the last two parts, published in 1917. Paul Fine has written a nice commentary [10].

1915

Ross R | Some a priori pathometric equations [11].

1916

Ross R | An application of the theory of probabilities to the study of a priori pathometry. Part I [12].

1917

  • Ross R & Hudson H | An application of the theory of probabilities to the study of a priori pathometry. Part II [13].

  • Ross R & Hudson H | An application of the theory of probabilities to the study of a priori pathometry. Part III [14].

1921

  • Ross R | The principle of repeated medication for curing infections [15]

  • Martini E | Berechnungen und Beobachtungen zur Epidemiologie und Bekämpfung der Malaria auf Grund von Balkanerfahrungen [16].

    • see Lotka’s commentary in 1923, below [17]

Analysis of Malaria Epidemiology

Analysis of Malaria Epidemiology – In 1923, Alfred Lotka published a 5-part analysis of Ross’s models. The fourth part was led by Sharpe.

  • Contribution to the Analysis of Malaria Epidemiology. I. General Part by Lotka [18].

  • Contribution to the Analysis of Malaria Epidemiology. II. General Part (continued). Comparison of Two Formulae given by Sir Ronald Ross, by Lotka [19].

  • Contribution to the Analysis of Malaria Epidemiology. III. Numerical Part, by Lotka [20].

  • Contribution to the Analysis of Malaria Epidemiology. IV. Incubation Lag, by Sharpe and Lotka [21].

  • Contribution to the Analysis of Malaria Epidemiology. V. Summary [22].

1923 - 1949

1923

Lotka AJ | Martini’s Equations for the Epidemiology of Immunising Diseases [17].

1947

Walton GA | On the control of malaria in Freetown, Sierra Leone; I. Plasmodium falciparum and Anopheles gambiae in relation to malaria occurring in infants [23].

Malariology (1949)

Malariology. A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint, edited by Mark Boyd, is two-volume, 1643 page collection of 70 essays from 65 authors [24].

  • Chapter 26: Boyd M | Epidemiology: Factors Related to the Definitive Host [25]

1950-1956

George Macdonald published 14 articles from 1950-1956.

1950

  • Macdonald G | The analysis of malaria parasite rates in infants [26].

  • Macdonald G | The analysis of infection rates in diseases in which superinfection occurs [27].

    • In 1975, Paul Fine wrote a very useful commentary on Macdonald’s formulation of the model [28].

1952

  • Macdonald G | The analysis of the sporozoite rate [29].

  • Macdonald G | The analysis of equilibrium in malaria [30].

1953

  • Macdonald G & Davidson G | Dose and cycle of insecticide applications in the control of malaria [31]

1955

  • Macdonald G | A new approach to the epidemiology of malaria [32]

  • Macdonald G | The measurement of malaria transmission [33]

  • Davidson G | Further studies of the basic factors concerned in the transmission of malaria [34]

1956

  • Macdonald G | Epidemiological basis of malaria control [35].

  • Macdonald G | Theory of the eradication of malaria [36].

Epidemiology & Control of Malaria

Macdonald G | The epidemiology and control of malaria [37]

The monumental studies by Lotka seemed indeed to bring the subject to an end, for no one could undertake mathematical analysis more skilfully or elaborately. (from the Preface)

1957 - 1969

1957

WHO | Expert Committee on Malaria, Sixth Report [38].

1959

  • Macdonald G | The dynamics of resistance to insecticides by anophelines [39].

1961

  • Macdonald G | Epidemiologic models in studies of vectorborne diseases [40].

Vectorial Capacity (1964)

See Vector Bionomics

  • Garrett-Jones C | Prognosis for interruption of malaria transmission through assessment of the mosquito’s vectorial capacity [41]

  • Garrett-Jones C | The human blood index of malaria vectors in relation to epidemiological assessment [42]

  • Garrett-Jones C | The assessment of insecticidal impact on the malaria mosquito’s vectorial capacity, from data on the proportion of parous females [43]

1964

The malaria parasite rate and interruption of transmission, led by George Macdonald [44].

1970 - 1981

The year 1970 marks an important turning point in malaria. In 19569, George Macdonald’s last paper was published posthumously, and the Global Malaria Eradication had come to an end.

1971

Dietz K. Malaria Models [45].

1974

Najera AJ. A critical review of the field application of a mathematical model of malaria eradication [46].

  • Macdonald’s model was field tested in Kankiya District, in northern Nigeria and deemed inadequate.

The Garki Model (1974)

Dietz K, …. A malaria model tested in the African savannah [47].

  • The Garki Model, a new mathematical model developed and field tested during the Garki Project [48].

1975

  • Dietz K | Models for parasitic disease control [49]

  • Fine PEM | Superinfection - a problem in formulating a problem, by Paul Fine [28].

    • discusses flaws in the formulation of Macdonald’s model for superinfection [27].

  • Fine PEM | Ross’s a priori pathometry - a perspective [10].

    • is a useful commentary on Ross and his philosophy of modeling.

1976

  • Dietz K | The incidence of infectious diseases under the influence of seasonal fluctuations [50].

  • Dutertre J | Etude d’un modèle épidémiologique appliqué au paludisme [51].

1977

Elderkin RH, … | On the steady state of an age dependent model for malaria. [52]

1978

  • Barbour AD | Macdonald’s model and the transmission of bilharzia [53].

  • Molineaux L, … | Further epidemiological evaluation of a malaria model [54].

Biomathematics of Malaria

Bailey NTJ | The Biomathematics of Malaria [55].

Bailey’s book was a comprehensive treatment of mathematical epidemiology for malaria up to that point.

  • Chapter 1: The world threat of malaria

  • Chapter 2: The epidemiology of malaria

  • Chapter 3: Historical perspectives

  • Chapter 4: The scope and role of biomathematics

  • Chapter 5: The theory and practice of modeling

  • Chapter 6: General theory of host-vector diseases

    • 6.2 - Deterministic Epidemics

    • 6.3 - Stochastic Epidemics

    • 6.4 - Small Epidemics in Large Populations

    • 6.5 - Spatial Spread

    • 6.6 - Endemic Models

  • Chapter 7: Elementary population dynamics of malaria

  • Chapter 8: Advances in the population dynamics of malaria

    • 8.2 - The Dietz-Molineaux-Thomas model

    • 8.3 - The model of Dutertre

    • 8.4 - The hybrid models of Nasell

    • 8.4 - The stochastic model of Bekessy, Molineaux & Storey

  • Chapter 9: Statistical esimation problems

  • Chapter 10: Control Theory

  • Chapter 11: Sensitivity Theory

1982 - 1987

1982

  • Aron J & May RM | The population dynamics of malaria [56].

    • A new model for parasite infection dynamics in mosquitoes was presented for the first time here. We present that model in a vignette

    • The paper also examines age-prevalence relationships largely using the Garki model [47]

  • Aron J | Malaria epidemiology and detectability [57]

1984

Nedelman J | Inoculation and recovery rates in the malaria model of Dietz, Molineaux, and Thomas. [58]

Malariology (1988)

Malaria: Principles and Practice of Malariology, edited by Walter Wernsdorfer and Ian McGregor, is a collection of 57 essays from 68 authors in two-volumes and 1818 pages [59]

  • Chapter 37: Dietz K | Mathematical models for transmission and control of malaria [60]

1988 - 1998

1989

  • Haile DG | Computer simulation of the effects of changes in weather patterns on vector-borne disease transmission [61].

  • Struchiner CJ, … | Modeling malaria vaccines I: New uses for old ideas [62].

  • Halloran ME, … | Modeling malaria vaccines. II: Population effects of stage-specific malaria vaccines dependent on natural boosting [63].

1990

Graves PM, … | Estimation of anopheline survival rate, vectorial capacity and mosquito infection probability from malaria vector infection rates in villages near Madang, Papua New Guinea [64]

1991

Koella JC | On the use of mathematical models of malaria transmission [65]

1992

Hellriegel B | Modelling the immune response to malaria with ecological concepts: short-term behaviour against long-term equilibrium [66].

1994

  • Dye C | Approaches to vector control: New and trusted. 5. The epidemiological context of vector control [67].

  • Dye C & Targett GAT | A theory of malaria vaccination [68].

Strain Theory (1994)

  • Gupta S & Day K | Clinical immunity to Plasmodium falciparum [69]

  • Gupta S & Day K | A strain theory of malaria transmission [70]

  • Gupta S, … | Antigenic diversity and the transmission dynamics of Plasmodium falciparum [71].

  • Gupta S, … | Parasite virulence and disease patterns in Plasmodium falciparum malaria [72]

  • Gupta S, … | Theoretical studies of the effects of heterogeneity in the parasite population on the transmission dynamics of malaria [73]

Intra-Host Models

Molineaux L & Dietz K | Review of intra-host models of malaria [74]

1999 - 2006

Open Malaria

2007 - 2010

malERA

2011 - 2019

2020 - 2025

References

1.
Ross R. On some peculiar pigmented cells found in two mosquitos fed on malarial blood. British medical journal. 1897;2: 1786–1788. Available: http://www.bmj.com/content/2/1929/1786.full.pdf
2.
Ross R. Mosquito brigades and how to organise them. London: George Philip & Son; 1902.
3.
Ross R. The Anti-Malaria Failure at Mian Mir. J R Army Med Corps. 1904;3: 210–212. doi:10.1136/jramc-03-02-15
4.
Ross R. The logical basis of the sanitary policy of mosquito reduction. Science. 1905;22: 689–699. doi:10.1126/science.22.570.689
5.
Ross R. Report on the Prevention of Malaria in Mauritius. London: Waterlow; 1908.
6.
Waite H. Mosquitoes and malaria. A study of the relation between the number of mosquitoes in a locality and the malaria rate. Biometrika. 1910;7: 421–436. doi:10.2307/2345376
7.
Ross R. The Prevention of Malaria. 2nd ed. London: John Murray; 1911.
8.
Ross R. Some quantitative studies in epidemiology. Nature. 1911;87: 466–467.
9.
Lotka AJ. Quantitative Studies in Epidemiology. Nature. 1912;88: 497–498. doi:10.1038/088497b0
10.
Fine PEM. Ross’s a priori pathometry - a perspective. Proc R Soc Med. 1975;68: 547–551. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=1105597
11.
Ross R. Some a priori pathometric equations. Br Med J. 1915;i: 546–547. doi:10.1136/bmj.1.2830.546
12.
Ross R. An application of the theory of probabilities to the study of a priori pathometry. Part I. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 1916;92: 204–230.
13.
Ross R, Hudson HP. An application of the theory of probabilities to the study of a priori pathometry. Part II. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences. 1917;93: 212–225.
14.
Ross R, Hudson H. An application of the theory of probabilities to the study of a priori pathometry. Part III. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 1917;93: 225–240. Available: http://adsabs.harvard.edu/abs/1917RSPSA..93..225R
15.
Ross R. The principle of repeated medication for curing infections. Br Med J. 1921;ii: 1–4. doi:10.1136/bmj.2.3157.1
16.
Martini E. Berechnungen und Beobachtungen zur Epidemiologie und Bekämpfung der Malaria auf Grund von Balkanerfahrungen. W. Gente; 1921.
17.
Lotka AJ. Martini’s equations for the epidemiology of immunising diseases. Nature. 1923;111: 633–634. doi:10.1038/111633a0
18.
Lotka AJ. Contribution to the Analysis of Malaria Epidemiology. I. General Part. American Journal of Epidemiology. 1923;3: 1–36. doi:10.1093/oxfordjournals.aje.a118963
19.
Lotka AJ. Contribution to the Analysis of Malaria Epidemiology. II. General Part (continued). Comparison of Two Formulae given by Sir Ronald Ross. American Journal of Epidemiology. 1923;3: 38–54. doi:10.1093/oxfordjournals.aje.a118965
20.
Lotka AJ. Contribution to the Analysis of Malaria Epidemiology. III. Numerical Part. American Journal of Epidemiology. 1923;3: 55–95. doi:10.1093/oxfordjournals.aje.a118966
21.
Sharpe FR, Lotka AJ. Contribution to the Analysis of Malaria Epidemiology. IV. Incubation lag. American Journal of Epidemiology. 1923;3: 96–112. doi:10.1093/oxfordjournals.aje.a118967
22.
Lotka AJ. Contribution to the Analysis of Malaria Epidemiology. V. Summary. American Journal of Epidemiology. 1923;3: 113–121. doi:10.1093/oxfordjournals.aje.a118964
23.
Walton GA. On the control of malaria in Freetown, Sierra Leone; I. Plasmodium falciparum and Anopheles gambiae in relation to malaria occurring in infants. Ann Trop Med Parasitol. 1947;41: 380–407. doi:10.1080/00034983.1947.11685341
24.
Boyd MF, editor. Malariology. A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint. Philadelphia, Pa.; London,: W. B. Saunders Co.; 1949. Available: https://www.cabdirect.org/cabdirect/abstract/19501000283
25.
Boyd MF. Chapter 26 - Epidemiology: Factors Related to the Definitive Host. Malariology A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint. Philadelphia: W. B. Saunders Company; 1949. pp. 608–697.
26.
Macdonald G. The analysis of malaria parasite rates in infants. Tropical Diseases Bulletin. 1950;47: 915–938.
27.
Macdonald G. The analysis of infection rates in diseases in which superinfection occurs. Tropical Diseases Bulletin. 1950;47: 907–915. Available: https://www.ncbi.nlm.nih.gov/pubmed/14798656
28.
Fine PEM. Superinfection - a problem in formulating a problem. Tropical Diseases Bulletin. 1975;75: 475–488.
29.
Macdonald G. The analysis of the sporozoite rate. Tropical Diseases Bulletin. 1952;49: 569–586. Available: https://www.ncbi.nlm.nih.gov/pubmed/14958825
30.
Macdonald G. The analysis of equilibrium in malaria. Tropical Diseases Bulletin. 1952;49: 813–829. Available: https://www.ncbi.nlm.nih.gov/pubmed/12995455
31.
Macdonald G, Davidson G. Dose and cycle of insecticide applications in the control of malaria. Bulletin of the World Health Organization. 1953;9: 785–812.
32.
Macdonald G. A new approach to the epidemiology of malaria. Indian J Malariol. 1955;9: 261–270. Available: https://www.ncbi.nlm.nih.gov/pubmed/13306284
33.
Macdonald G. The measurement of malaria transmission. Proceedings of the Royal Society of Medicine. 1955;48: 295–302.
34.
Davidson G. Further studies of the basic factors concerned in the transmission of malaria. Trans R Soc Trop Med Hyg. 1955;49: 339–350. doi:10.1016/0035-9203(55)90056-0
35.
Macdonald G. Epidemiological basis of malaria control. Bull World Health Organ. 1956;15: 613–626. Available: https://www.ncbi.nlm.nih.gov/pubmed/13404439
36.
Macdonald G. Theory of the eradication of malaria. Bull World Health Organ. 1956;15: 369–387. Available: https://www.ncbi.nlm.nih.gov/pubmed/13404426
37.
Macdonald G. The epidemiology and control of malaria. Oxford university press; 1957. Available: https://www.cabdirect.org/cabdirect/abstract/19582900392
38.
Expert Committee on Malaria} {WHO. Expert Committee on Malaria, Sixth Report. Athens: Geneva: Palais des Nations.; 1957. Report No.: 123. Available: https://www.cabdirect.org/cabdirect/abstract/19582900403
39.
Macdonald G. The dynamics of resistance to insecticides by anophelines. Riv Parassitol. 1959;20: 305–315.
40.
Macdonald G. Epidemiologic models in studies of vectorborne diseases. Public Health Rep. 1961;76: 753–764. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=13764730
41.
Garrett-Jones C. Prognosis for interruption of malaria transmission through assessment of the mosquito’s vectorial capacity. Nature. 1964;204: 1173–1175. doi:10.1038/2041173a0
42.
Garrett-Jones C. The human blood index of malaria vectors in relation to epidemiological assessment. Bull World Health Organ. 1964;30: 241–261. Available: https://www.ncbi.nlm.nih.gov/pubmed/14153413
43.
Garrett-Jones C, Grab B. The assessment of insecticidal impact on the malaria mosquito’s vectorial capacity, from data on the proportion of parous females. Bull World Health Organ. 1964;31: 71–86. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=14230896
44.
Macdonald G, Goeckel GW. The malaria parasite rate and interruption of transmission. Bull World Health Organ. 1964;31: 365–377. Available: https://www.ncbi.nlm.nih.gov/pubmed/14267746
45.
Dietz K. Malaria Models. Adv Appl Probab. 1971;3: 208–210. doi:10.2307/1426159
46.
Nájera JA. A critical review of the field application of a mathematical model of malaria eradication. Bull World Health Organ. 1974;50: 449–457. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=4156197
47.
Dietz K, Molineaux L, Thomas A. A malaria model tested in the African savannah. Bull World Health Organ. 1974;50: 347–357. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=4613512
48.
Molineaux L, Gramiccia G. The Garki Project: Research on the Epidemiology and Control of Malaria in the Sudan Savanna of West Africa. World Health Organization; 1980. Available: https://apps.who.int/iris/handle/10665/40316
49.
Dietz K. Models for parasitic disease control. Bull Int Stat Inst. 1975;46: 531–544.
50.
Dietz K. The incidence of infectious diseases under the influence of seasonal fluctuations. In: Berger J, Bühler WJ, Repges R, Tautu P, editors. Mathematical models in medicine. Berlin, Heidelberg: Springer Berlin Heidelberg; 1976. pp. 1–15.
51.
Dutertre J. Etude d’un modèle épidémiologique appliqué au paludisme. Ann Soc Belg Med Trop. 1976;56: 127–141. Available: http://lib.itg.be/open/ASBMT/1976/1976asbm0127.pdf
52.
Elderkin RH, Berkowitz DP, Farris FA, Gunn CF, Hickernell FJ, Kass SN, et al. On the steady state of an age dependent model for malaria. In: Lakshmikantham V, editor. Nonlinear Systems and Applications. Academic Press; 1977. pp. 491–512. doi:10.1016/B978-0-12-434150-0.50047-3
53.
Barbour AD. Macdonald’s model and the transmission of bilharzia. Transactions of the Royal Society of Tropical Medicine and Hygiene. 1978;72: 6–15. doi:10.1016/0035-9203(78)90290-0
54.
Molineaux L, Dietz K, Thomas A. Further epidemiological evaluation of a malaria model. Bull World Health Organ. 1978;56: 565–571. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=365384
55.
Bailey NTJ. The Biomathematics of Malaria. Oxford: Charles Griffin & Company Ltd.; 1982. Available: https://play.google.com/store/books/details?id=4MCAQgAACAAJ
56.
Aron JL, May RM. The population dynamics of malaria. In: Anderson RM, editor. The Population Dynamics of Infectious Diseases: Theory and Applications. Boston, MA: Springer US; 1982. pp. 139–179. Available: https://doi.org/10.1007/978-1-4899-2901-3_5
57.
Aron JL. Malaria epidemiology and detectability. Trans R Soc Trop Med Hyg. 1982;76: 595–601. doi:10.1016/0035-9203(82)90219-x
58.
Nedelman J. Inoculation and recovery rates in the malaria model of Dietz, Molineaux, and Thomas. Math Biosci. 1984;69: 209–233. doi:10.1016/0025-5564(84)90086-5
59.
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Dietz K. Mathematical models for transmission and control of malaria. In: Wernsdorfer W, McGregor IA, editors. Malaria: Principles and Practice of Malariology. New York: Churchill Livingstone; 1988. pp. 1091–1133. Available: http://www.worldcat.org/title/malaria-1/oclc/310943664
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Halloran ME, Struchiner CJ, Spielman A. Modeling malaria vaccines II: Population effects of stage-specific malaria vaccines dependent on natural boosting. Mathematical Biosciences. 1989;94: 115–149. doi:10.1016/0025-5564(89)90074-6
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Koella JC. On the use of mathematical models of malaria transmission. Acta Trop. 1991;49: 1–25. doi:10.1016/0001-706x(91)90026-g
66.
Hellriegel B. Modelling the immune response to malaria with ecological concepts: Short-term behaviour against long-term equilibrium. Proc Biol Sci. 1992;250: 249–256. doi:10.1098/rspb.1992.0156
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Dye C. Approaches to vector control: New and trusted. 5. The epidemiological context of vector control. Trans R Soc Trop Med Hyg. 1994;88: 147–149. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=8036654
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Gupta S, Day K. Clinical immunity to Plasmodium falciparum. Parasitol Today. 1994;10: 64; author reply 64–5. doi:10.1016/0169-4758(94)90396-4
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Gupta S, Day KP. A strain theory of malaria transmission. Parasitol Today. 1994;10: 476–481. doi:10.1016/0169-4758(94)90160-0
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Gupta S, Trenholme K, Anderson RM, Day KP. Antigenic diversity and the transmission dynamics of Plasmodium falciparum. Science. 1994;263: 961–963. doi:10.1126/science.8310293
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Gupta S, Hill AV, Kwiatkowski D, Greenwood AM, Greenwood BM, Day KP. Parasite virulence and disease patterns in Plasmodium falciparum malaria. Proc Natl Acad Sci U S A. 1994;91: 3715–3719. doi:10.1073/pnas.91.9.3715
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Gupta S, Swinton J, Anderson RM. Theoretical studies of the effects of heterogeneity in the parasite population on the transmission dynamics of malaria. Proceedings of the Royal Society of London B: Biological Sciences. 1994;256: 231–238. doi:10.1098/rspb.1994.0075
74.
Molineaux L, Dietz K. Review of intra-host models of malaria. Parassitologia. 1999;41: 221–231. Available: http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&id=10697860&retmode=ref&cmd=prlinks