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 Literature, letters, judged to be "eminently distinguished in their subject". ...

(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 A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the Medical education, study, Med ...

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, and application of this knowledge to prevent diseases. It is a cornerstone ...

who pioneered the use of mathematical methods in

epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and Risk factor (epidemiology), determinants of health and disease conditions in a defined population, and application of this knowledge to prevent dise ...

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 Co ...

(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."

Biography

McKendrick was born at on 8 September 1876, in

Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...

, the fifth and last child of

John Gray McKendrick John Gray McKendrick (12 August 1841 – 2 January 1926) was a Scottish physiologist. He served as Regius Professor of Physiology at the University of Glasgow from 1876 to 1906, and was co-founder of the Physiological Society. Early life McKe ...

FRS, a distinguished

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

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

John Souttar McKendrick Dr John Souttar McKendrick FRSE (1874-1946) was a Scottish physician from the eminent McKendrick family. He served as President of the Royal College of Physicians and Surgeons of Glasgow in 1939. Life He was born in 1874 the eldest son of John G ...

(1874–1946). He was educated at

Kelvinside Academy Kelvinside Academy is a private 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 six ...

then trained as a doctor at the

University of Glasgow The University of Glasgow (abbreviated as ''Glas.'' in Post-nominal letters, post-nominals; ) is a Public university, public research university in Glasgow, Scotland. Founded by papal bull in , it is the List of oldest universities in continuous ...

qualifying MB ChB in 1900. He then was commissioned in the British Army and joined the

Indian Medical Service The Indian Medical Service (IMS) was a military medical service in British India, which also had some civilian functions. It served during the two World Wars, and remained in existence until the independence of India in 1947. Many of its officer ...

. At the rank of Lt Colonel he led an expedition into

Somaliland Somaliland, officially the Republic of Somaliland, is an List of states with limited recognition, unrecognised country in the Horn of Africa. It is located in the southern coast of the Gulf of Aden and bordered by Djibouti to the northwest, E ...

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 (, ) 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 for anthrax and rabies. Th ...

Kasauli Kasauli is a town and cantonment, located in the Solan district of 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 Punjab (; ; also romanised as Panjāb or Panj-Āb) is a geopolitical, cultural, and historical region in South Asia. It is located in the northwestern part of the Indian subcontinent, comprising areas of modern-day eastern Pakistan and no ...

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 set the specialty training standards for physicians in the United Kingdom. It was established by royal charter i ...

. 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, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

. In 1911, McKendrick rediscovered the logistic equation 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 (RSE) 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 establis ...

. 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 Pat ...

Ralph Stockman Ralph Stockman (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 anaemia. Life Stoc ...

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 1933, he was elected a member of the

Aesculapian Club The Aesculapian Club of Edinburgh is one of the oldest medical dining clubs in the world. It was founded in April 1773 by Dr. Andrew Duncan. Membership of the club is limited to 11 Fellows of the Royal College of Physicians of Edinburgh and ...

. 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 stat ...

. 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 involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

. 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 in a probability space, where the index of the family often has the interpretation of time. Stoc ...

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 ''An Introduction to Probability Theory 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 b ...

(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 immunizing infectious disease over time as it is transmitted through a population based on characteristics of infectivity and recovery, under a st ...

, a general theory of infectious disease transmission. He died on May 30, 1943, aged 68, in

Carrbridge Carrbridge (, ) is a village in Badenoch and Strathspey in the Scottish Highlands. It lies off the A9 on the A938, west of Skye of Curr and southeast of Tomatin, near Bogroy. It has the oldest stone bridge in the Highlands and the nearby a ...

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.

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 Amateur mathematicians