Lt Col Anderson Gray McKendrick DSc

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This soc ...

(8 September 1876 – 30 May 1943) was a

Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-European language family native to Scotland *Scottish English *Scottish national identity, the Scottish ide ...

military physician and

epidemiologist Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evid ...

who pioneered the use of mathematical methods in epidemiology.

Irwin Irwin may refer to: Places ;United States * Irwin, California * Irwin, Idaho * Irwin, Illinois * Irwin, Iowa * Irwin, Nebraska * Irwin, Ohio * Irwin, Pennsylvania * Irwin, South Carolina * Irwin County, Georgia * Irwin Township, Venango Cou ...

(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."

Life

McKendrick was born at 2 Chester Street in Edinburgh the fifth and last child of

John Gray McKendrick John Gray McKendrick FRS FRSE FRCPE LLD (12 August 1841 – 2 January 1926) was a distinguished Scottish physiologist. He was born and studied in Aberdeen, Scotland, and served as Regius Professor of Physiology at the University of Glasgow fr ...

FRS, a distinguished physiologist, and his wife, Mary Souttar. His older brother was John Souttar McKendrick

(1874-1946). He was educated at Kelvinside Academy then trained as a doctor at the University of Glasgow qualifying MB ChB in 1900. He then was commissioned in the British Army and joined the Indian Medical Service. At the rank of Lt Colonel he led an expedition into Somaliland in 1903/4 as part of what was then known as the Dervish Wars. He later worked with

Ronald Ross Sir Ronald Ross (13 May 1857 – 16 September 1932) was a British medical doctor who received the Nobel Prize for Physiology or Medicine in 1902 for his work on the transmission of malaria, becoming the first British Nobel laureate, and the f ...

and eventually would continue his work on mathematical epidemiology. His primary interest was in research and he was director of the Pasteur Institute at

Kasauli Kasauli is a town and cantonment, located in Solan district in the Indian state of Himachal Pradesh. The cantonment was established by the British Raj in 1842 as a Colonial hill station,Sharma, Ambika"Architecture of Kasauli churches" ''The ...

in the Punjab 1914–1920. 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 The Royal College of Physicians of Edinburgh (RCPE) is a medical royal college in Scotland. It is one of three organisations that sets the specialty training standards for physicians in the United Kingdom. It was established by Royal charter ...

. He held this post for the rest of his life. McKendrick's career as a mathematical epidemiologist began in India. In 1911, McKendrick rediscovered the

logistic equation A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the ...

and fit it to bacterial growth data. In 1912 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were James Oliver,

Diarmid Noel Paton Diarmid Noël Paton, (19 March 1859 – 30 September 1928), known as Noël Paton, was a Scottish physician and academic. From 1906 to 1928, he was the Regius Professor of Physiology at the University of Glasgow. Personal life and education ...

Ralph Stockman Dr Ralph Stockman MD LLD (3 August 1861–27 February 1946) was a Scottish Regius Professor of Medicine and Therapeutics , Professor of Materia Medica and Therapeutics at the University of Glasgow. He was an expert on iron deficiency anaemi ...

and

Cargill Gilston Knott Cargill Gilston Knott FRS, FRSE LLD (30 June 1856 – 26 October 1922) was a Scottish physicist and mathematician who was a pioneer in seismological research. He spent his early career in Japan. He later became a Fellow of the Royal Society, ...

. He served as the Society's Vice President 1933-36. In 1914 he published a paper in which he gave equations for the pure birth process and a particular

birth–death process The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state ...

. In 1924 he was elected a Fellow of the

. After his return to Scotland he published more. His 1926 paper, 'Applications of mathematics to medical problems' was particularly impressive, including the widely used McKendrick–Von Foerster

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

\frac + \frac = - \mu(t,a) n.

Some of this paper's other results for

stochastic models In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

of epidemics and population growth were rediscovered by

William Feller William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Early life and education Feller was born in Zagreb to Ida Oemichen-Perc, a C ...

in 1939. Feller remarks in his Introduction to the Theory of Probability and Its Applications (3rd edition p. 450), "It is unfortunate that this remarkable paper passed practically unnoticed." In 1927 McKendrick began a collaboration with

William Ogilvy Kermack William Ogilvy Kermack FRS FRSE FRIC (26 April 1898 – 20 July 1970) was a Scottish biochemist. He made mathematical studies of epidemic spread and established links between environmental factors and specified diseases. He is noteworthy for ...

(1898–1970) which produced a notable series of papers on the Kermack–McKendrick theory, a general theory of infectious disease transmission. 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. McKendric
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 in

J. O. Irwin Joseph Oscar Irwin (17 December 1898 – 27 July 1982) was a 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 disti ...

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.

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.

References

External links

* There is a photograph at
A. G. McKendrick
on th

page. 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
Royal Society citation for John Gray McKendrick

Royal Society citation for William Ogilvy Kermack

Photo of Kermack

KERMACK, William Ogilvy
{{DEFAULTSORT:McKendrick, Anderson Gray 1876 births 1943 deaths Medical doctors from Edinburgh People educated at Kelvinside Academy Alumni of the University of Glasgow 20th-century Scottish medical doctors British public health doctors Scottish statisticians Indian Medical Service officers Military personnel from Edinburgh Fellows of the Royal Society of Edinburgh British epidemiologists