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.