3.2 Mosquito Bionomics

Macdonald made several important contributions to the mathematical study of malaria. Ross’s original formulation remained the standard until Macdonald’s paper on the sporozoite rate [42]. Because of it’s historical interest, we’ll discuss Ross’s formulation in the discussion of [Macdonald’s Model], in part, to make it clear why Macdonald’s contribution was significant enough to get his name attached.

In the 1950s, George Macdonald published a set of papers describing malaria transmission dynamics and control, culminating in publicataion of a book The Epidemiology and Control of Malaria [67].

In 1950, Macdonald published a new model with human malaria superinfection [57] and a synthetic review of malaria epidemiology [62]. In 1952, Macdonald published a synthetic review of medical entomology [42] and introduced the concept of a basic reproductive number, \(R_0\) [43].

As a side note, it’s highly likely that Macdonald was aware of Lotka’s demographic concept of \(R_0\), as well as his work with Sharpe on delay differential equations [68], though we have been unable to find a single line where Macdonald gives Lotka the credit. For these reasons, and others, the equations ought to be described as the Ross-Lotka-Macdonald model.

References

42.
Macdonald G. The analysis of the sporozoite rate. Trop Dis Bull. 1952;49: 569–586. Available: https://www.ncbi.nlm.nih.gov/pubmed/14958825
43.
Macdonald G. The analysis of equilibrium in malaria. Trop Dis Bull. 1952;49: 813–829. Available: https://www.ncbi.nlm.nih.gov/pubmed/12995455
57.
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
62.
Macdonald G. The analysis of malaria parasite rates in infants. Tropical diseases bulletin. 1950;47: 915–938.
67.
Macdonald G. The epidemiology and control of malaria. Oxford university press; 1957. Available: https://www.cabdirect.org/cabdirect/abstract/19582900392
68.
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