Anderson Gray McKendrick
Encyclopedia
Anderson Gray McKendrick (September 8, 1876 - May 30, 1943) was a Scottish
physician
and epidemiologist pioneered the use of mathematical methods in epidemiology
. Irwin
(see below) commented on the quality of his work, "Although an amateur, he was a brilliant mathematician, with a far greater insight than many professionals."
McKendrick was born in Edinburgh
the fifth and last child of John Gray McKendrick FRS, a distinguished physiologist. The son trained as a doctor at the University of Glasgow
and joined the Indian Medical Service. He worked with Ronald Ross
and eventually would continue his work on mathematical epidemiology. His primary interest was in research and he became director of the Pasteur Institute
at Kausali in the Punjab
. He was invalided home to Britain in 1920 and settled in Edinburgh where he became Superintendent of the Laboratory of the Royal College of Physicians of Edinburgh
. He held this post for the rest of his life.
McKendrick's career as a mathematical epidemiologist began in India
. In 1914 he published a paper in which he gave equations for the pure birth process and a particular birth-death process
. After his return to Scotland he published more. His 1926 paper, 'Applications of mathematics to medical problems' was particularly impressive. Some of its results for stochastic models of epidemics and population growth were rediscovered by William Feller
in 1939. Feller remarks in his Introduction to the Theory of Probability & its Applications (3rd edition p. 450), "It is unfortunate that this remarkable paper passed practically unnoticed." The same paper is also the earliest reference in Dempster et al.'s 1977 paper that defined and popularized the EM algorithm (Expectation-maximization algorithm
) In 1927 McKendrick began a collaboration with W. O. Kermack (1898 - 1970) which produced a notable series of papers. The first paper (1927) gave the differential equations for a deterministic general epidemic
.
W. M. Hirsch gives this picture of the man: "McKendrick was a truly Christian gentleman, a tall and handsome man, brilliant in mind, kind and modest in person, a skilful counsellor and administrator who gave of himself and knew how to enable others."
J. O. Irwin
The Place of Mathematics in Medical and Biological Statistics, Journal of the Royal Statistical Society
. Series A (General), Vol. 126, No. 1. (1963), pp. 1-45.
There is a modern presentation of one of the Kermack-McKendrick models in
McKendrick's father was elected to the Royal Society
, as was Kermack his co-worker
Scottish people
The Scottish people , or Scots, are a nation and ethnic group native to Scotland. Historically they emerged from an amalgamation of the Picts and Gaels, incorporating neighbouring Britons to the south as well as invading Germanic peoples such as the Anglo-Saxons and the Norse.In modern use,...
physician
Physician
A physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury and other physical and mental impairments...
and epidemiologist pioneered the use of mathematical methods in epidemiology
Epidemiology
Epidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
. Irwin
Joseph Oscar Irwin
Joseph Oscar Irwin British statistician who advanced the use of statistical methods in biological assay and other fields of laboratory medicine. Irwin’s grasp of modern mathematical statistics distinguished him not only from older medical statisticians like Major Greenwood but contemporaries like...
(see below) commented on the quality of his work, "Although an amateur, he was a brilliant mathematician, with a far greater insight than many professionals."
McKendrick was born in Edinburgh
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...
the fifth and last child of John Gray McKendrick FRS, a distinguished physiologist. The son trained as a doctor at the University of Glasgow
University of Glasgow
The University of Glasgow is the fourth-oldest university in the English-speaking world and one of Scotland's four ancient universities. Located in Glasgow, the university was founded in 1451 and is presently one of seventeen British higher education institutions ranked amongst the top 100 of the...
and joined the Indian Medical Service. He worked with Ronald Ross
Ronald Ross
Sir Ronald Ross KCB FRS was a British doctor who received the Nobel Prize for Physiology or Medicine in 1902 for his work on malaria. He was the first Indian-born person to win a Nobel Prize...
and eventually would continue his work on mathematical epidemiology. His primary interest was in research and he became director of the Pasteur Institute
Pasteur Institute
The Pasteur Institute is a French non-profit private foundation dedicated to the study of biology, micro-organisms, diseases, and vaccines. It is named after Louis Pasteur, who made some of the greatest breakthroughs in modern medicine at the time, including pasteurization and vaccines for anthrax...
at Kausali in the Punjab
Punjab region
The Punjab , also spelled Panjab |water]]s"), is a geographical region straddling the border between Pakistan and India which includes Punjab province in Pakistan and the states of the Punjab, Haryana, Himachal Pradesh, Chandigarh and some northern parts of the National Capital Territory of Delhi...
. He was invalided home to Britain in 1920 and settled in Edinburgh where he became Superintendent of the Laboratory of the Royal College of Physicians of Edinburgh
Royal College of Physicians of Edinburgh
The Royal College of Physicians of Edinburgh was established in the 17th century. While the RCPE is based in Edinburgh, it is by no means just a Scottish professional body - more than half of its 7,700 Fellows, Members, Associates and Affiliates live and practice medicine outside Scotland, in 86...
. He held this post for the rest of his life.
McKendrick's career as a mathematical epidemiologist began in India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
. In 1914 he published a paper in which he gave equations for the pure birth process and a particular birth-death process
Birth-death process
The birth–death process is a special case of continuous-time Markov process where the states represent the current size of a population and where the transitions are limited to births and deaths...
. After his return to Scotland he published more. His 1926 paper, 'Applications of mathematics to medical problems' was particularly impressive. Some of its results for stochastic models of epidemics and population growth were rediscovered by William Feller
William Feller
William Feller born Vilibald Srećko Feller , was a Croatian-American mathematician specializing in probability theory.-Early life and education:...
in 1939. Feller remarks in his Introduction to the Theory of Probability & its Applications (3rd edition p. 450), "It is unfortunate that this remarkable paper passed practically unnoticed." The same paper is also the earliest reference in Dempster et al.'s 1977 paper that defined and popularized the EM algorithm (Expectation-maximization algorithm
Expectation-maximization algorithm
In statistics, an expectation–maximization algorithm is an iterative method for finding maximum likelihood or maximum a posteriori estimates of parameters in statistical models, where the model depends on unobserved latent variables...
) In 1927 McKendrick began a collaboration with W. O. Kermack (1898 - 1970) which produced a notable series of papers. The first paper (1927) gave the differential equations for a deterministic general epidemic
Epidemic
In epidemiology, an epidemic , occurs when new cases of a certain disease, in a given human population, and during a given period, substantially exceed what is expected based on recent experience...
.
W. M. Hirsch gives this picture of the man: "McKendrick was a truly Christian gentleman, a tall and handsome man, brilliant in mind, kind and modest in person, a skilful counsellor and administrator who gave of himself and knew how to enable others."
Selected works
- A. G. McKendrick 'Applications of mathematics to medical problems' Kapil Proceedings of the Edinburgh Mathematical Society, vol 44, (1925-6), pp. 1-34. Reprinted with commentary in S. Kotz & N. L. Johnson (Editors) (1997) Breakthroughs in Statistics: Volume III New York Springer.
- W. O. Kermack; A. G. McKendrick “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society of London. Series A, Vol. 115, (1927), pp. 700-721.
- W. O. Kermack; A. G. McKendrick “Contributions to the Mathematical Theory of Epidemics. II. The Problem of Endemicity,” Proceedings of the Royal Society of London. Series A, Vol. 138, (1932) pp. 55-83.
- W. O. Kermack; A. G. McKendrick “Contributions to the Mathematical Theory of Epidemics. III. Further Studies of the Problem of Endemicity,” Proceedings of the Royal Society of London. Series A, Vol. 141, (1933), pp. 94-122.
Commentary
There is an account of McKendrick's Applications paper inJ. O. Irwin
Joseph Oscar Irwin
Joseph Oscar Irwin British statistician who advanced the use of statistical methods in biological assay and other fields of laboratory medicine. Irwin’s grasp of modern mathematical statistics distinguished him not only from older medical statisticians like Major Greenwood but contemporaries like...
The Place of Mathematics in Medical and Biological Statistics, Journal of the Royal Statistical Society
Journal of the Royal Statistical Society
The Journal of the Royal Statistical Society is a series of three peer-reviewed statistics journals published by Blackwell Publishing for the London-based Royal Statistical Society.- History :...
. Series A (General), Vol. 126, No. 1. (1963), pp. 1-45.
Biography
- Warren M. Hirsch (2004) McKendrick, Anderson Gray (1876–1943), Oxford Dictionary of National Biography, Oxford University Press.
- Gani, J. (2001) Anderson Gray McKendrick, Statisticians of the Centuries (ed. C. C. Heyde and E. Seneta) pp. 323-327. New York: Springer.
External links
There is a photograph at- A. G. McKendrick on the Portraits of Statisticians page.
There is a modern presentation of one of the Kermack-McKendrick models in
McKendrick's father was elected to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, as was Kermack his co-worker
