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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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