IvOTka: contribution to epidemiology 77 



of the subsequent fate of the afifected persons after they pass 

 beyond the period qi q^ of infectivity, or of their condition before 

 they enter it, provided only that they enter it with a given value 

 of P {Qi}- This may appear at first sight somewhat surprising, 

 but on reflection is found to be in accord with reason. 



The case discussed above is strictly analogous to the "Prob- 

 lem in Age-Distribution" which has been treated by Prof. F. R. 

 Sharpe and the writer elsewhere.*^ The development given 

 above is what the present author had in mind when he wrote, 

 in a previous publication:^ 



Brief reflection shows that we can apply to this case (endemic disease) 

 a mathematical treatment precisely analogous to that of the growth 

 of a population ; for we may think of the diseased portion of the popula- 

 tion as a separate aggregate, into which new individuals are recruited 

 by fresh infections, just as new individuals enter an ordinary popula- 

 tion by procreation. On the other hand, members are continually 

 eliminated from the aggregate, first by deaths, secondly by recoveries. 

 On the basis of these considerations formulae can without difficulty 

 be established between the factors enumerated above. Such general 

 formulae, however, involve certain functions which are unknown, and 

 the determination of which by statistical methods would at best present 

 great difficulties. 



In conclusion it may not be out of place to remark that, aside 

 from mathematical similarity, what places the two cases — ^growth 

 of a population and spread of a disease — in the same class, is 

 the physical circumstance that both are cases of autocatalytic 

 or autocatakinetic growth. The rate of growth at any instant 

 increases with the size of the existing nucleus or focus, other 

 things equal. 



* See also Sharps and Lotka. Phil. Mag., Apr. 191 1, p. 436. 

 ^ Nature, Feb. 8, 1912, p. 497. 



