Macdonald & Eradication
Draft – this is a work in progress. please be patient.
Here, we provide some commentary about George Macdonald’s publications starting in 1950 and culminating in 1957 with the publication of The Epidemiology and Control of Malaria. Ironically, Macdonald was not very good at math, and he never published his full model as a system of differential equations. In the next essay, we present a Ross-Macdonald Model.
Not a Mathematician
In setting the stage for George Macdonald’s contributions to malaria, we quote from the preface of his book (page xi in [1]):
The mathematical studies of Ross appeared an attactive approach to new explanation, but experiment showed they did not complete the picture or provide explanation, and their elaboration by Waite, McKendrick, Lotka and others gave no more clarificiation. The monumental studies by Lotka seemed indeed to bring the subject to an end, for no one could undertake mathematical analysis more skilfully or elaborately.
Nevertheless, the logic of the approach seemed sound. It should be possible to examine the interaction of numerical factors by numerical methods, and so to see how they might be integrated in nature. Considerable audactiy was needed for one who is not a mathematician to re-open the subject, but it seemed permissible particularly because the previous analysis showed that the fault could not like in mathematical tecnhique. The premises on which that analysis was made were therefore examined, and were identical through all the works.
From this, we learn some very important things. First, Ross’s mathematical models were not well-regarded in Macdonald’s day. Second, Macdonald was aware of Lotka’s mathematical analysis of Ross’s equations. It stands to reason that Lotka’s work on the basic reproductive number in human demography was the source for his work on a formula for \(R_0\). Third, Macdonald did not consider himself to be a mathematician.
At the end, he points out that the models had all made basically the same assumptions, and that some of those assumptions were wrong. Macdonald is setting up his own explanation of superinfection [2], but the same argument could apply to many other phenomena that Macdonald did not challenge.
Malariology
In 1949, the year before George Macdonald started publishing his influential essays [3]
Malariology. A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint.
edited by Mark Boyd, is collection of 70 essays from 65 authors in two volumes and 1643 pages [1].