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 soci ...

(8 September 1876 – 30 May 1943) was a Scottish military

physician A physician (American English), medical practitioner (Commonwealth English), medical doctor, or simply doctor, is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through th ...

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 evidenc ...

who pioneered the use of mathematical methods in

epidemiology 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 evidenc ...

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 County ...

(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 Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...

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 Physiology (; ) is the scientific study of functions and mechanisms in a living system. As a sub-discipline of biology, physiology focuses on how organisms, organ systems, individual organs, cells, and biomolecules carry out the chemical a ...

, and his wife, Mary Souttar. His older brother was John Souttar McKendrick

(1874-1946). He was educated at

Kelvinside Academy Kelvinside Academy is an independent day school in Glasgow, Scotland, founded in 1878. It has a capacity of over 600 pupils and spans two years of Nursery, six years of Junior School (primary school), a transition year of Senior Preparatory, and ...

then trained as a doctor at the

University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

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 Somaliland,; ar, صوماليلاند ', ' officially the Republic of Somaliland,, ar, جمهورية صوماليلاند, link=no ''Jumhūrīyat Ṣūmālīlānd'' is a ''de facto'' sovereign state in the Horn of Africa, still conside ...

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 The Pasteur Institute (french: Institut Pasteur) 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 invented pasteurization and vaccines f ...

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 Trib ...

in the

Punjab Punjab (; Punjabi: پنجاب ; ਪੰਜਾਬ ; ; also romanised as ''Panjāb'' or ''Panj-Āb'') is a geopolitical, cultural, and historical region in South Asia, specifically in the northern part of the Indian subcontinent, comprising ...

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 India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

. 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 The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

. 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 P ...

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

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. 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 calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

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

Some of this paper's other results for stochastic models 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 Cro ...

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 Kermack–McKendrick theory is a hypothesis that predicts the number and distribution of cases of an infectious disease as it is transmitted through a population over time. Building on the research of Ronald Ross and Hilda Hudson, A. G. McKendrick ...

, 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 The Place of Mathematics in Medical and Biological Statistics,

Journal of the Royal Statistical Society The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founded ...

. 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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

, 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