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      Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

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          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.

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          PROGNOSIS FOR INTERRUPTION OF MALARIA TRANSMISSION THROUGH ASSESSMENT OF THE MOSQUITO'S VECTORIAL CAPACITY.

          C. Garrett (1964)
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            Larval source management for malaria control in Africa: myths and reality

            As malaria declines in many African countries there is a growing realization that new interventions need to be added to the front-line vector control tools of long-lasting impregnated nets (LLINs) and indoor residual spraying (IRS) that target adult mosquitoes indoors. Larval source management (LSM) provides the dual benefits of not only reducing numbers of house-entering mosquitoes, but, importantly, also those that bite outdoors. Large-scale LSM was a highly effective method of malaria control in the first half of the twentieth century, but was largely disbanded in favour of IRS with DDT. Today LSM continues to be used in large-scale mosquito abatement programmes in North America and Europe, but has only recently been tested in a few trials of malaria control in contemporary Africa. The results from these trials show that hand-application of larvicides can reduce transmission by 70-90% in settings where mosquito larval habitats are defined but is largely ineffectual where habitats are so extensive that not all of them can be covered on foot, such as areas that experience substantial flooding. Importantly recent evidence shows that LSM can be an effective method of malaria control, especially when combined with LLINs. Nevertheless, there are a number of misconceptions or even myths that hamper the advocacy for LSM by leading international institutions and the uptake of LSM by Malaria Control Programmes. Many argue that LSM is not feasible in Africa due to the high number of small and temporary larval habitats for Anopheles gambiae that are difficult to find and treat promptly. Reference is often made to the Ross-Macdonald model to reinforce the view that larval control is ineffective. This paper challenges the notion that LSM cannot be successfully used for malaria control in African transmission settings by highlighting historical and recent successes, discussing its potential in an integrated vector management approach working towards malaria elimination and critically reviewing the most common arguments that are used against the adoption of LSM.
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              THE HUMAN BLOOD INDEX OF MALARIA VECTORS IN RELATION TO EPIDEMIOLOGICAL ASSESSMENT.

              C. Garrett (1963)
              The human blood index, or estimated proportion of the blood meals of a mosquito population obtained from man, is provisionally assessed for certain anophelines from blood-meal samples collected during the period 1959-62 and subjected to precipitin testing at the Lister Institute. In malaria eradication programmes this index is relevant to epidemiological assessment and to the modification of measures to interrupt transmission, since a mosquito's vectorial capacity and the malaria reproduction rate both vary as the square of the human blood index.There are serious difficulties in achieving representative sampling for this index and in interpreting the index obtained. These are discussed in some detail. In practice, the human blood index is often best estimated by applying the unweighted mean of a part-sample collected from human dwellings and one from other types of resting-place.Applying this calculation to the samples under review, it appears that DDT exerts a moderate, and dieldrin a more pronounced, impact on the human blood index of Anopheles gambiae and A. funestus; such an effect, indeed, may be general in house-visiting anophelines. Some 18 anopheline species are tentatively graded as having low, medium or high natural human blood indices. Regular and careful sampling, combined with recording of all relevant information, is recommended in view of the epidemiological and operational importance of the human blood index in assessment of eradication programmes.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Pathog
                PLoS Pathog
                plos
                plospath
                PLoS Pathogens
                Public Library of Science (San Francisco, USA )
                1553-7366
                1553-7374
                April 2012
                April 2012
                5 April 2012
                : 8
                : 4
                : e1002588
                Affiliations
                [1 ]Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America
                [2 ]Malaria Research Institute, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America
                [3 ]Fogarty International Center, National Institutes of Health, Bethesda, Maryland, United States of America
                [4 ]Spatial Ecology and Epidemiology Group, Department of Zoology, Oxford University, Oxford, United Kingdom
                [5 ]Center for Vectorborne Diseases, University of California, Davis, California, United States of America
                [6 ]Department of Pathology, Microbiology, and Immunology, School of Veterinary Medicine, University of California, Davis, California, United States of America
                [7 ]Department of Entomology, University of California, Davis, California, United States of America
                International Centre for Genetic Engineering and Biotechnology, India
                Author notes
                Article
                PPATHOGENS-D-11-02708
                10.1371/journal.ppat.1002588
                3320609
                22496640
                d0477df0-1732-4749-81ba-b45498c41c9c
                This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
                History
                Page count
                Pages: 13
                Categories
                Review
                Biology
                Population Biology
                Population Dynamics
                Population Modeling

                Infectious disease & Microbiology
                Infectious disease & Microbiology

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