58 lotka: discontinuous evolution 



assumes a somewhat more favorable aspect if we are satisfied 

 with the discussion of the simple special case of a stationary popu- 

 lation, in which the disease also is supposed to have reached 

 equilibrium. 



We may then proceed as follows: 



Let A" be the total number of the population, and 



A"i the number afflicted with the disease. 

 Let S = Ns be the total number of deaths per unit of time, 

 and let 

 Si = Ni Si be the number of deaths per unit of time, due 

 to the disease considered. 



Let Aicri =A"i — be the total number of individuals eliminated 



T 



from the aggregate of diseased persons 

 per unit of time from all causes, including 

 deaths by the disease under consideration, 

 by other diseases, and also recoveries. 



When a stationary condition is reached, <n must be equal to 

 the reciprocal of the mean duration L of the disease. In this 

 case we have, then 



N lSl =N^ (27) 



Furthermore, if 7 is a factor indicating that fraction of the 

 total deaths, which is due to the disease considered, then 



N 1 s 1 =N 1 ^ = yNs (28) 



Hence 



Ai yLs 



or, solving for L 



(29) 



A T 



L = ~- (30) 



N ys 



By the way of a numerical example, let us substitute in the 

 formula thus obtained some data gathered from the statistics 



