Malaria Models and Theory
An Annotated, Chronological Bibliography of Mathematical Theory for Malaria
Also see:
1900-1917
The Prevention of Malaria – In the first 15 years after Ronald Ross identified malaria parasites in the mosquito mid gut, he turned his attention to the prevention of malaria and published the first three mathematical models of malaria. In 1912, Lotka proposed a solution to the model Ross published in Nature.
1905 – The logical basis of the sanitary policy of mosquito reduction, by Ross [1], was the first mathematical model describing malaria control.
1908 – Report on the Prevention of Malaria in Mauritius, by Ross [2].
- This is the first mathematical model describing mosquito-borne pathogen transmission.
1910 – Mosquitoes and malaria. A study of the relation between the number of mosquitoes in a locality and the malaria rate, by H Waite [3].
- This is an analysis of Ross’s 1908 model [2].
1911 – Ross published the second model of malaria transmission in the \(2^{nd}\) edition of The Prevention of Malaria and in Nature
The Prevention of Malaria, by Ross [4]. Note that the model is missing from the \(1^{st}\) edition.
Some quantitative studies in epidemiology, by Ross [5]
1912 – Quantitative Studies in Epidemiology, by Aflred Lotka [6],
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 [7],
1916-1917 An application of the theory of probabilities to the study of a priori pathometry 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 [8].
An application of the theory of probabilities to the study of a priori pathometry. Part I. by Ronald Ross [9],
An application of the theory of probabilities to the study of a priori pathometry. Part II, by Ronald Ross and Hilda Hudson [10],
An application of the theory of probabilities to the study of a priori pathometry. Part III, by Ronald Ross and Hilda Hudson [11],
1923
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 [12].
Contribution to the Analysis of Malaria Epidemiology. II. General Part (continued). Comparison of Two Formulae given by Sir Ronald Ross, by Lotka [13].
Contribution to the Analysis of Malaria Epidemiology. III. Numerical Part, by Lotka [14].
Contribution to the Analysis of Malaria Epidemiology. IV. Incubation Lag, by Sharpe and Lotka [15].
Contribution to the Analysis of Malaria Epidemiology. V. Summary [16].
1950 - 1969
The Epidemiology and Control of Malaria – in the 1950s, Macdonald published
1950
The analysis of malaria parasite rates in infants, by Macdonald [17].
- See Vector Bionomics
The analysis of infection rates in diseases in which superinfection occurs, by Macdonald
1952
The analysis of the sporozoite rate by George Macdonald [18].
The analysis of equilibrium in malaria by George Macdonald [19].
1957
- The epidemiology and control of malaria, by George Macdonald [20]
1964
The malaria parasite rate and interruption of transmission, led by George Macdonald [21].
Prognosis for interruption of malaria transmission through assessment of the mosquito’s vectorial capacity, by C Garrett-Jones [22]
- See Vector Bionomics
1970 - 1981
1971
1974
A critical review of the field application of a mathematical model of malaria eradication, by Najera [23].
- Macdonald’s model was field tested in Kankiya District, in northern Nigeria and deemed inadequate.
A malaria model tested in the African savannah, led by Klaus Dietz [24].
1975
[26]
In 1975, Paul EM Fine published two commentaries on the early development of malaria theory.
1976
Models for parasitic disease control, by Dietz [29]
Etude d’un modèle épidémiologique appliqué au paludisme. [30]
1977 - On the steady state of an age dependent model for malaria. [31]
1978 - Further epidemiological evaluation of a malaria model. [32]
1982
The Biomathematics of Malaria, by Norman Bailey [33], is a comprehensive review 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 - 1989
1982
The population dynamics of malaria, by Joan Aron and Robert May [34].
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 [24]
[35]
1984 - [36]