Abstract
Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.
Highlights
Background and IntroductionMosquitoes transmit the pathogens that cause malaria, filariasis, dengue, yellow fever, West Nile fever, Rift Valley fever, and dozens of other infectious diseases of humans, domestic animals, and wildlife [1]
Ronald Ross discussed malaria with Manson while in the United Kingdom, but conducted his research while serving in a military post in India, and in 1897 he demonstrated that mosquitoes transmit malaria parasites [4,5]
Ross argued that mosquito population densities could be reduced through larval control and combined with other measures to prevent mosquito-transmitted diseases [6]
Summary
Mosquitoes transmit the pathogens that cause malaria, filariasis, dengue, yellow fever, West Nile fever, Rift Valley fever, and dozens of other infectious diseases of humans, domestic animals, and wildlife [1]. The model has played the classical role of a scientific theory; it is a deliberately simplified set of concepts that serves as a basis for studying mosquitoborne pathogen transmission Like other theories, it has formed the starting point for a dialogue about methods, for defining what should be emphasized and measured, and for building new models of mosquito-borne disease transmission. Mathematical models were a way to codify, refine, and communicate the quantitative logic of biological phenomena, especially mosquitoborne pathogen transmission, in a form that was rigorous and testable In his correspondence with Manson in 1897, before successfully demonstrating that mosquitoes transmit malaria, Ross was already reasoning quantitatively about his own fever [39]: An incubation period of two or three days... implies to mathematical demonstration an access or ingress of many millions of parasites at the moment of infection. Ross’s formula (making some liberal allowances in the interpretation of parameters) is equivalent to the following: Common Notation Ross (1st) [22] Waite [41] Lotka [42] Ross (2nd) [23] Sharpe & Lotka [46] Macdonald [55,67] Aron & May (1st) [91] Smith & McKenzie [93] Aron & May (2nd) [91] Anderson & May [92]
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