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Lt Col '''Anderson Gray McKendrick''' DSc [[FRSE]] (8 September 1876 – 30 May 1943) was a [[Scottish people|Scottish]] military [[physician]] and [[epidemiologist]] who pioneered the use of mathematical methods in [[epidemiology]]. [[Joseph Oscar Irwin|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."

==Life==

McKendrick was born at 2 Chester Street<ref>Edinburgh and Leith Post Office Directory 1876-77</ref> in [[Edinburgh]] the fifth and last child of [[John Gray McKendrick]] FRS, a distinguished [[physiologist]], and his wife, Mary Souttar. His older brother was [[John Souttar McKendrick]] [[FRSE]] (1874-1946).

He was educated at [[Kelvinside Academy]] then trained as a doctor at the [[University of Glasgow]] qualifying MB ChB in 1900.<ref name="Herald 31May1943">{{cite news |url=https://news.google.com/newspapers?id=dTlAAAAAIBAJ&pg=3922%2C1565609 |title=Lieut. Colonel A. G. M'Kendrick |work=[[The Glasgow Herald]] |date=31 May 1943 |page=4 |accessdate=1 May 2017}}</ref> 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.<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X|url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|access-date=7 July 2017|archive-url=https://web.archive.org/web/20160304074135/https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|archive-date=4 March 2016|url-status=dead}}</ref>

He later worked with [[Ronald Ross]] 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]] in the [[Punjab region|Punjab]] 1914–1920.<ref name="Herald 31May1943"/> 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 1911, McKendrick rediscovered the [[Logistic function|logistic equation]] and fit it to bacterial growth data.<ref>{{cite journal |title=XLV.—The Rate of Multiplication of Micro-organisms: A Mathematical Study|first1=A. G. |last1=McKendrick |first2=M. |last2=Kesava Pai |journal=Proceedings of the Royal Society of Edinburgh |volume=31 |date=January 1912 |pages=649–653 |doi=10.1017/S0370164600025426|url=https://zenodo.org/record/1543653 }}</ref> In 1912 he was elected a Fellow of the [[Royal Society of Edinburgh]]. His proposers were James Oliver, [[Diarmid Noel Paton]], [[Ralph Stockman]] and [[Cargill Gilston Knott]]. He served as the Society's Vice President 1933-36.<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X|url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|access-date=7 July 2017|archive-url=https://web.archive.org/web/20160304074135/https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|archive-date=4 March 2016|url-status=dead}}</ref>

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 [[Royal College of Physicians of Edinburgh]]. After his return to Scotland he published more. His 1926 paper, 'Applications of mathematics to medical problems' was particularly impressive, including
the widely used [[Von Foerster equation|McKendrick–Von Foerster]] [[partial differential equation]]

: <math> \frac{\partial n}{\partial t} + \frac{\partial n}{\partial a} = - \mu(t,a) n. </math>


Some of this paper's other 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 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]] (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. McKendrick [https://dx.doi.org/10.1017/S0013091500034428 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,” [http://rspa.royalsocietypublishing.org/content/115/772/700.full.pdf+html 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,” [http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-56234 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

[[Joseph Oscar Irwin|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.

==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==
{{Reflist}}

==External links==
* {{MacTutor Biography|id=McKendrick}}

There is a photograph at
* [http://www.york.ac.uk/depts/maths/histstat/people/mckendrick.gif A. G. McKendrick] on the [http://www.york.ac.uk/depts/maths/histstat/people/welcome.htm Portraits of Statisticians] page.

There is a modern presentation of one of the Kermack–McKendrick models in
* [http://mathworld.wolfram.com/Kermack-McKendrickModel.html Mathworld: Kermack–McKendrick model]

McKendrick's father was elected to the [[Royal Society]], as was Kermack his co-worker
* [http://www.royalsoc.ac.uk/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqSearch=RefNo=='EC/1884/15'&dsqDb=Catalog Royal Society citation for John Gray McKendrick]
* [http://www.royalsoc.ac.uk/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqSearch=RefNo=='EC/1944/11'&dsqDb=Catalog Royal Society citation for William Ogilvy Kermack]
* [http://www.royalsoc.ac.uk/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=ImageView.tcl&dsqDb=Catalog&dsqImage=Kermack%20W%20O,%20GA%20WS%202134.jpg Photo of Kermack]
* [https://web.archive.org/web/20120204040527/http://www.open.ac.uk/ou5/Arts/chemists/person.cfm?SearchID=3340 KERMACK, William Ogilvy]

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

Anderson Gray McKendrick - Revision history

Bot at 15:42, 27 September 2021