H. Waite 
423 
since probably many mosquitoes never succeed in biting men at all, and of those 
that do succeed, only a few will have bitten a particular individual. Hence the 
average number of anophelines which have bitten the suitably infected persons 
during the month will be haim. 
Now if any of these insects are, in their turn, to infect human beings, they 
must survive for at least a week or ten days, in order to give time for the 
parasites to mature within them ; and by no means all of them will survive so 
long. Let s be the average proportion of anophelines which can survive for that 
period ; then sbairn will be the number of infected mosquitoes which have 
survived long enough to infect men in their turn, where s is also a fraction. But 
not all of these will find opportunities to bite human beings again, though they 
have survived long enough to do so. Let f be the proportion which succeed in 
biting. Then fshaim will be the average number of infecting anophelines which 
succeed in biting men ; also, if each of these bite a separate person and only one 
person, the same expression will denote the average number of persons bitten by 
infecting mosquitoes during the month. Call this number n. The most probable 
distribution of the n bites between malarial and non-malarial persons will be in 
the ratio m ih; so that the number of new infections during the month will be 
fsbaimh/p, or nhjp*. 
Now each time a healthy person is bitten by an infecting mosquito the number 
of malarial patients is increased by unity, while the bites inflicted on those who 
are already suffering from the disease make no difference in the number of cases. 
This is equivalent to increasing m and decreasing h by hjp for each bite. 
[By taking mean values in the above I am assuming that if 
z = F {x-^^, X2, ... X ,1), 
then z may be taken = F {x-^,x.i, ...x.,^, and I have been led to make this 
assumption in a first investigation by finding that the modal values of the 
distribution approximate very closely to the means in a number of particular cases 
fully worked out.] 
Recovery Rate. The ratio of the number of recoveries to the total number of 
malaria cases during any period is called the Recovery Rate for that period. 
Professor Ross has estimated that of a given number of infected persons 50 are 
ill after three months, that is, the recovery rate is '5 per three months. 
If wio be the number of cases at the beginning of the period, m, , m.,, m^, at the 
ends of the first, second and third months respectively, and r the recovery rate 
per month, 
r/(, = ?;?o — "hi" — ''io (1 — '■)' 
m.2 — vii (1 - r) = niu ( 1 — ?•)-, 
= m.,{l — r) = ^Hq (1 — 
* Professor Eoss assumes that to a first ai^proximation n will be the number of new cases in the 
month. 
54—2 
