Mathematical Theory for Malaria: A Bibliography

An Annotated, Chronological Bibliography of Mathematical Theory for Malaria

Reviews

1982 – The Biomathematics of Malaria, by Norman Bailey [1], is a comprehensive review of mathematical epidemiology for malaria up to that point.

1982 – The population dynamics of malaria, by Joan Aron and Robert May [2], is a very useful review of malaria. One of the models is covered in a vignette.

1988 – Mathematical models for transmission and control of malaria by Klaus Dietz [3],

1991 – On the use of mathematical models of malaria transmission [4]

1999 – Review of intra-host models of malaria by Louis Molineaux and Klaus Dietz [5],

2012 – Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens, led by David Smith [SmithDL2012_RossMacdonald?], reviews development theory for malaria including Ross and Macdonald.

2013 – A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010, led by Robert Reiner and Alex Perkins [6].

Commentaries

2000 – Why Model Malaria? by Ellis McKenzie [7],

2014 – Recasting the theory of mosquito-borne pathogen transmission dynamics and control, led by David Smith [SmithDL2014Recasting?],

1905-1912

The Prevention of Malaria – Over a few years, Ross published the first three mathematical models of malaria.

1905 – The logical basis of the sanitary policy of mosquito reduction, by Ronald Ross [8], was the first mathematical model describing malaria control.

1908 – Report on the Prevention of Malaria in Mauritius, by Ronald Ross [9], has the first mathematical model…

1910 – Mosquitoes and malaria. A study of the relation between the number of mosquitoes in a locality and the malaria rate, by H Waite [10], analyzes Ross’s 1908 model.

1911 – The Prevention of Malaria. 2nd ed., by Ronald Ross [11]

1911 – Some quantitative studies in epidemiology, by Ronald Ross [12]

1912 – Quantitative Studies in Epidemiology, by Aflred Lotka [13],

1915-1917

A priori Pathometry – Ronald Ross teamed up with Hilda Hudson, a mathematician from Cambridge University, to establish some mathematical foundations for what is now called mathematical epidemiology.

1915 – Some a priori pathometric equations by Ronald Ross [14],

1916 – An application of the theory of probabilities to the study of a priori pathometry. Part I. by Ronald Ross [15],

1917 – An application of the theory of probabilities to the study of a priori pathometry. Part II, by Ronald Ross and Hilda Hudson [16],

1917 – An application of the theory of probabilities to the study of a priori pathometry. Part III, by Ronald Ross and Hilda Hudson [17],

1975 – Ross’s a priori pathometry - a perspective, by Paul Fine [18], is a useful commentary on Ross and his philosophy of modeling.

1923

Analysis of Malaria Epidemiology – In 1923, Alfred Lotka published a 5-part analysis of Ross’s models

  1. General Part by Lotka [19], …

  2. General Part (continued). Comparison of Two Formulae given by Sir Ronald Ross [20],…

  3. Numerical Part [21], …

  4. Incubation Lag [22],

  5. Summary [23],

1950s

The Epidemiology and Control of Malaria

1950

  • The analysis of malaria parasite rates in infants, by George Macdonald… [24].

  • The analysis of infection rates in diseases in which superinfection occurs, by George Macdonald … [25].

1952

  • The analysis of the sporozoite rate, by George Macdonald… [26].

  • The analysis of equilibrium in malaria, by George Macdonald… [27].

1957

  • The epidemiology and control of malaria, by George Macdonald [28]

1960s

1964

  • The malaria parasite rate and interruption of transmission, led by George Macdonald [29],

  • The human blood index of malaria vectors in relation to epidemiological assessment. by C. Garrett-Jones [Garrett-JonesC1964HBI?]

  • Prognosis for interruption of malaria transmission through assessment of the mosquito’s vectorial capacity, by C Garrett-Jones [Garrett-JonesC1964VC?]

1965

1969

1970s

1974

  • A malaria model tested in the African savannah, led by Klaus Dietz [32], describes the Garki Model, a new mathematical model developed and field tested during the Garki Project [33]. The model was developed, in part, after the Macdonald’s model had been field tested in Kankiya District, in northern Nigeria and deemed inadequate [34].

1975

  • Superinfection - a problem in formulating a problem, by Paul Fine [35], discusses flaws in the formulation of Macdonald’s model for superinfection [25].

1980s

1980

1982

  • The Biomathematics of Malaria, by Norman Bailey [1], is a comprehensive review of mathematical epidemiology for malaria up to that point.

  • The population dynamics of malaria, by Joan Aron and Robert May, is a very useful review of malaria (aron_may.html) [2].

    • 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 [32]

1990s

2000s

References

1.
Bailey NTJ. The Biomathematics of Malaria. Oxford: Charles Griffin & Company Ltd.; 1982. Available: https://play.google.com/store/books/details?id=4MCAQgAACAAJ
2.
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
3.
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
4.
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
5.
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
6.
Reiner RC, Perkins TA, Barker CM, Niu T, Chaves LF, Ellis AM, et al. A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010. J R Soc Interface. 2013;10: 20120921.
7.
McKenzie FE. Why model malaria? Parasitol Today. 2000;16: 511–516. doi:10.1016/s0169-4758(00)01789-0
8.
Ross R. The logical basis of the sanitary policy of mosquito reduction. Science. 1905;22: 689–699. doi:10.1126/science.22.570.689
9.
Ross R. Report on the Prevention of Malaria in Mauritius. London: Waterlow; 1908.
10.
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
11.
Ross R. The Prevention of Malaria. 2nd ed. London: John Murray; 1911.
12.
Ross R. Some quantitative studies in epidemiology. Nature. 1911;87: 466–467.
13.
Lotka AJ. Quantitative Studies in Epidemiology. Nature. 1912;88: 497–498. doi:10.1038/088497b0
14.
Ross R. Some a priori pathometric equations. Br Med J. 1915;i: 546–547. doi:10.1136/bmj.1.2830.546
15.
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.
16.
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.
17.
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
18.
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
19.
Lotka AJ. Contributions to the analysis of malaria epidemiology. Am J Hyg. 1923;3 (Suppl. 1): 1–121.
20.
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
21.
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
22.
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
23.
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
24.
Macdonald G. The analysis of malaria parasite rates in infants. Tropical diseases bulletin. 1950;47: 915–938.
25.
Macdonald G. The analysis of infection rates in diseases in which superinfection occurs. Trop Dis Bull. 1950;47: 907–915. Available: https://www.ncbi.nlm.nih.gov/pubmed/14798656
26.
Macdonald G. The analysis of the sporozoite rate. Trop Dis Bull. 1952;49: 569–586. Available: https://www.ncbi.nlm.nih.gov/pubmed/14958825
27.
Macdonald G. The analysis of equilibrium in malaria. Trop Dis Bull. 1952;49: 813–829. Available: https://www.ncbi.nlm.nih.gov/pubmed/12995455
28.
Macdonald G. The epidemiology and control of malaria. Oxford university press; 1957. Available: https://www.cabdirect.org/cabdirect/abstract/19582900392
29.
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
30.
De Zulueta J, Garrett-Jones C. An Investigation of the Persistence of Malaria Transmission in Mexico. Am J Trop Med Hyg. 1965;14: 63–77. doi:10.4269/ajtmh.1965.14.63
31.
Garrett-Jones C, Shidrawi GR. Malaria vectorial capacity of a population of Anopheles gambiae: An exercise in epidemiological entomology. Bull World Health Organ. 1969;40: 531–545. Available: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=5306719
32.
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
33.
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
34.
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
35.
Fine PEM. Superinfection - a problem in formulating a problem. Tropical Diseases Bulletin. 1975;75: 475–488.
36.
Garrett-Jones C, Boreham PFL, Pant CP. Feeding habits of anophelines (Diptera: Culicidae) in 1971–78, with reference to the human blood index: A review. Bull Entomol Res. 1980;70: 165–185. doi:10.1017/S0007485300007422