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\noindent{\bf Pyotr Dimitrievich EN'KO}\\
b. 15 November 1844 - d. 6 March 1916 (o.s.)
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\noindent{\bf Summary.} En'ko was a Russian physician whose probabilistic
modelling and data
analysis of measles epidemics in the late 1880s anticipated the work of Reed and
Frost in the 1920s.
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In 1760, Daniel Bernoulli (q.v.)
produced a model for the number of susceptibles in
a cohort of individuals exposed to smallpox; this model did not involve what
is now understood as the spread of infection by homogeneous mixing (mass
action) in a
susceptible population. Dietz (1988) has made an excellent case for Pyotr
Dimitrievich
En'ko's paper (1889) as the first to discuss the elements of a genuine
epidemic model,
namely the chain binomial; this was developed some forty years later by Reed
and Frost
in the USA (see Abbey, 1952 and Frost, 1976).
En'ko was born in St. Petersburg in 1844, the son of a member of the
nobility in
the Chernigov region, and a Saxon mother. In an autobiographical sketch (in
Pushkin's
Dom at the Vengerov Archives, St. Petersburg), En'ko mentions that the family
rose in
the 17th and 18th centuries to achieve wealth and social importance. He was
first
educated at the school attached to the Imperial Medical and Surgical Academy
of St.
Petersburg, where he was greatly influenced by his mathematics teacher, and by
the
school principal Bardovskiy. The best pupils were encouraged to pursue topics
outside
the school curriculum, and to read widely in the school's excellent library.
He later
studied medicine at the Academy itself, and graduated from it in 1867. He
began his
medical career as an intern at the Zagorodnaya Hospital in 1869, and in 1871
transferred
to the St. Petersburg Alexander Institute, whose senior doctor he became in
1874. He
worked as a physician among children, and in his book, Moshkovskiy (1950)
mentions that
he was concerned with ``the clinical and epidemiological aspects of children's
infections,
physiology and the hygiene of schools".
En'ko organized the first institutional medical station in Lipetsk, south
of Moscow
in 1885, remaining at its head for several years. He then set up a similar
station in
Gapsal. In 1901 he was named Director of the Imperial School for Deaf-Mutes
in St.
Petersburg. He was decorated for his work, ending his career as an official
of fairly
high rank in the hierarchy of the imperial public service. He was married,
with 3
daughters and two sons. He was a person clearly ahead of his times, and
expressed
disappointment that his ``natural method of education" for deaf-mutes found
little
support among his colleagues, despite its success with patients. He appears
to have
been equally unsuccessful in persuading participants at the all-Russian 1910
meeting
on the education of deaf-mutes in Moscow, of the merits of his method.
While practising medicine in St Petersburg, En'ko continued his researches,
and
presented a dissertation on revaccination (published in Russian in 1873) for
the
Doctorate in Medicine of the Medical Faculty of the University of St.
Petersburg. This
was not accepted, but by accident he found out that Professor Minding of the
Tsarist
University of Dorpat (now Tartu in Estonia) was interested in probability, and
arranged
to consult him. Minding understood his approach to the problem and approved
his original
methods of analysis. In the autumn of 1874, he travelled to the University of
Dorpat to
take an examination in German, and was then awarded his Doctorate in Medicine
by the
Medical Faculty for the German version of his dissertation (1874).
Few further details are known about his later life; he continued to
practise
medicine, and between 1873 and 1913 authored some 71 works, not all of them on
strictly
scientific topics. Of his many scientific papers, most are in Russian, but
some are
in German and French. The topics were quite diverse: revaccination, the
degeneration
of vaccines, muscle contraction, the thorax, the brightness of light,
respiratory organs,
the artificial feeding of newborn babies, hygiene in daily life,
vegetarianism, the
teaching of deaf-mutes. His two main works on epidemic problems are his paper
on
susceptibility to measles and scarlatina (1887), and his famous contribution
(1889)
on the course of epidemics (see Dietz's English translation, 1989). He died
in 1916
during the First World War, just before the Russian Revolution of 1917.
We give a brief description of En'ko's contribution to epidemic modelling.
Consider the spread of an infection
in a
population of size $N_t$ of whom $C_t$ are infectives and $S_t$ are
susceptibles in
discrete time $t > 0$. En'ko argued, on the assumption of homogeneous mixing,
that a
particular susceptible would have a chance
$$ P_{C_t} = C_t /(N_t - 1) $$
of making contact with an infective. Thus, if $A$ is the number of actual
contacts
of infectives with susceptibles, then the probability of making at least one
contact is
$$ a_t = 1 - [(N_t - 1 - C_t)/(N_t - 1)]^{A_t}. $$
Hence, assuming that new infectives occur according to the binomial
distribution,
the total number of new infectives will have a mean ${a_t}{S_t}$. In En'ko's
model, $A_t$
can vary depending on the propensity of individuals to gather in groups, or
lead a
solitary existence.
En'ko gathered daily data on several measles epidemics at the St Petersburg
Alexander Institute and the Educational College for the Daughters of the
Nobility,
carefully recording the population size $N_t$ and the initial number of cases
$C_{0}$. He
estimated the number of contacts $A_t$ , varying the value until he obtained
good fits of
the data to the theory, and graphing the results. His work foreshadows the
Reed-Frost
chain binomial model of 1928, and entitles him to be considered as the first
epidemic
modeller in the modern sense of the word. En'ko's achievement is a
vindication of
the value of a broad education, resulting in the competent use of mathematical
methods by medical doctors; it is also a reminder that original thinking
can occur
in very unsettled circumstances, such as those prevalent in Russia through
much of En'ko's life.
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\noindent
{\it Acknowledgement}. My thanks are due to Dr G. Sh. Tsitsiashvili
and Professor K. Dietz for their help in preparing this article.
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\begin{thebibliography}{3}
\bibitem{1}
Abbey, Helen (1952). An examination of the Reed-Frost theory of epidemics.
{\it Human Biology} {\bf 24}, 201-233.
\bibitem{2}
Dietz, K. (1988). The first epidemic model: a historical note on P.D. En'ko.
{\it Australian Journal of Statistics} {\bf 30A}, 56-65.
\bibitem{3}
En'ko, P.D. (1874). Ueber die Anwendung der Analyse auf die Frage von der
Revaccination. Doctoral Dissertation, University of Dorpat.
\bibitem{4}
En'ko, P.D. (1887). On the susceptibility to measles and scarlatina. Vrach. St.
Petersburg, VIII, 723, 744 (in Russian).
\bibitem{5}
En'ko, P.D. (1889). On the course of epidemics of some infectious diseases.
Vrach. St. Petersburg, X, 1008-10010, 1039-1042, 1061-1063 (in Russian). English
translation by Dietz, K. (1989) {\it International Journal of Epidemiology} {\bf 18}, 749-755.
\bibitem{6}
Frost, W.H. (1976). Some conceptions of epidemics in general. {\it American Journal of
Epidemiology} {\bf 103}, 141-151.
\bibitem{7}
Moshkovskiy, Sh.D. (1950). {\it Basic Laws of Malaria Epidemiology}. Izdat. AMN SSSR,
Moscow (in Russian).
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Additional biographical material and a follow-up of En'ko's work may be found
in:
\bibitem{8}
Ondar, Ch.O. (1973). About the first applications of probability theory to
medicine.
{\it Sbornik Istorija i Metologija Jestestvennych Nauk} {\bf 14},
159-166 (in Russian).
\bibitem{9}
Tovstitskiy, K.V. (1906). Application of probability theory to the statistics
of vaccination. {\it Matematicheskii Sbornik} {\bf 26}, 545-598 (in Russian).
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\hfill{J. Gani}
\end{thebibliography}
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