Malaria Modeling

Reviews & Commentaries


Other Bibliographies: Mathematical Models | Vector Bionomics


1916

Ross R | An application of the theory of probabilities to the study of a priori pathometry. Part I [1].

It is somewhat surprising that so little mathematical work should have been done on the subject of epidemics, and, indeed, on the distribution of diseases in general. Not only is the theme of immediate importance to humanity, but it is one which is fundamentally connected with numbers, while vast masses of statistics have long been awaiting proper examination. But, more than this, many and indeed the principal problems of epidemiology on which preventive measures largely depend, such as the rate of infection, the frequency of outbreaks, and the loss of immunity, can scarcely ever be resolved by any other methods than those of analysis.

The whole subject is capable of study by two distinct methods which are used in other branches of science, which are complementary of each other, and which should converge towards the same results – the a posteriori and the a prioi methods. In the former we commence with observed statistics, endeavour to fit analytical laws to them, and so work backwards to the underlying cause (as done in much statistical work of the day); and in the latter we assume a knowledge of the causes, construct our differential equations on that supposition, follow up the logical consequences, and finally test the calculated results by comparing them with the observed statistics.

1957

Macdonald G | The epidemiology and control of malaria [2]

1969

Bruce-Chwatt LJ | Quantitative epidemiology of tropical diseases. [3].

1975

Fine PEM | Superinfection - a problem in formulating a problem, by Paul Fine [4].

Fine PEM | Ross’s a priori pathometry - a perspective [5].

1976

Bruce-Chwatt LJ | Swellengrabel oration: Mathematical models in the epidemiology and control of malaria [6]

1982

Bailey NTJ | The Biomathematics of Malaria [7]. This book is a comprehensive review of mathematical epidemiology for malaria from its inception through the 1970s.

Aron JL & May RM | The population dynamics of malaria [8]. This book chapter is a very useful review of malaria. One of the models is covered in a vignette.

1985

Molineaux L | The pros and cons of modelling malaria transmission [9]

1988

Dietz K | Mathematical models for transmission and control of malaria [10].

  • Chapter 37 in the two volume set, Malaria: Principles and Practice of Malariology

1991

Koella J | On the use of mathematical models of malaria transmission [11]

1999

Molineaux L & Dietz K | Review of intra-host models of malaria [12]

2000

McKenzie FE | Why Model Malaria? [13].

2011

Mandal S, … | Mathematical models of malaria – a review [14].

2012

Smith DL, … | Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens [15].

  • A review of development of theory for malaria including Ross and Macdonald.

  • The supporting information includes an annotated bibliography

2013

Reiner RC Jr, Perkins TA, … | A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010 [16].

2014

Smith DL, … | Recasting the theory of mosquito-borne pathogen transmission dynamics and control [17].

2018

Smith NR, … | Agent-based models of malaria transmission: A systematic review [18].

2021

Camponovo F, … | Mechanistic within-host models of the asexual Plasmodium falciparum infection: A review and analytical assessment [19].

References

1.
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.
2.
Macdonald G. The epidemiology and control of malaria. Oxford university press; 1957. Available: https://www.cabdirect.org/cabdirect/abstract/19582900392
3.
Bruce-Chwatt LJ. Quantitative epidemiology of tropical diseases. Transactions of the Royal Society of Tropical Medicine and Hygiene. 1969;63: 131–143. Available: http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&id=4892495&retmode=ref&cmd=prlinks
4.
Fine PEM. Superinfection - a problem in formulating a problem. Tropical Diseases Bulletin. 1975;75: 475–488.
5.
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
6.
Bruce-Chwatt LJ. Swellengrabel oration: Mathematical models in the epidemiology and control of malaria. Tropical and geographical medicine. 1976;28: 1–8.
7.
Bailey NTJ. The Biomathematics of Malaria. Oxford: Charles Griffin & Company Ltd.; 1982. Available: https://play.google.com/store/books/details?id=4MCAQgAACAAJ
8.
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
9.
Molineaux L. The pros and cons of modelling malaria transmission. Trans R Soc Trop Med Hyg. 1985;79: 743–747. doi:10.1016/0035-9203(85)90107-5
10.
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
11.
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
12.
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
13.
McKenzie FE. Why model malaria? Parasitology Today. 2000;16: 511–516. doi:10.1016/s0169-4758(00)01789-0
14.
Mandal S, Sarkar RR, Sinha S. Mathematical models of malaria–a review. Malar J. 2011;10: 202. doi:10.1186/1475-2875-10-202
15.
Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog. 2012;8: e1002588. doi:10.1371/journal.ppat.1002588
16.
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.
17.
Smith DL, Perkins TA, Reiner RC, Barker CM, Niu T, Chaves LF, et al. Recasting the theory of mosquito-borne pathogen transmission dynamics and control. Trans R Soc Trop Med Hyg. 2014;108: 185–197. doi:10.1093/trstmh/tru026
18.
Smith NR, Trauer JM, Gambhir M, Richards JS, Maude RJ, Keith JM, et al. Agent-based models of malaria transmission: A systematic review. Malar J. 2018;17: 299. doi:10.1186/s12936-018-2442-y
19.
Camponovo F, Lee TE, Russell JR, Burgert L, Gerardin J, Penny MA. Mechanistic within-host models of the asexual Plasmodium falciparum infection: A review and analytical assessment. Malaria Journal. 2021;20: 309. doi:10.1186/s12936-021-03813-z