Several basic mathematical models of malaria transmission have been published across the years [1,2]. In the following, we walk through several of them:
In 1908, Ross wrote Report on the Prevention of Malaria in Mauritius and presented the first mathematical model of malaria transmission [3]. In 1910, it was reviewed by Waite [4]. In 1923, Lotka analyzed this model in some detail [5,6]. This model is discussed an implemented in SimBA (To Do).
In 1911, Ross published his second model of malaria transmission. It appeared in the \(2^{nd}\) edition of The Prevention of Malaria [7] and in an article in Nature [8]. In 1912, Lotka published a closed form solution in Nature [9]. In 1923, Lotka analyzed this model in some detail [5,6,10,11]. This model is discussed an implemented in SimBA (To Do).
In 1923, Sharpe and Lotka extended Ross’s model to consider delays for latency in both the mosquito and human hosts [12]. This model is discussed an implemented in SimBA (To Do).
Macdonald published a set of articles in 1950 [13,14] and 1952 [15,16]. Macdonald’s models have been implemented in SimBA (To Do).
In 1982, Aron & May presented a new model for malaria transmission dynamics and control in a form that is more extensible [17]. That model has been implemented in SimBA (To Do).
References
1.
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
2.
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.
3.
Ross R. Report on the Prevention of Malaria in Mauritius. London: Waterlow; 1908.
4.
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
5.
Lotka AJ. Contributions to the analysis of malaria epidemiology. Am J Hyg. 1923;3 (Suppl. 1): 1–121.
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.
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
12.
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
13.
Macdonald G. The analysis of malaria parasite rates in infants. Tropical diseases bulletin. 1950;47: 915–938.
17.
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