424 
Mosquitoes and Malaria 
But = m.a(l — •5), 
.: (l-7f=-5, 
log (1 - ?•) ^ i log -5 
= 1-899657, 
.-. l-r=-7937, 
and .■. ?•=:: "2063 per month. 
In the numerical examples it will be necessary to know the recovery rate for 
the average period between two consecutive bites. Suppose there are n bites in 
a month and is the recovery rate for the period between two consecutive bites, 
then, as before, 
(1 - rf = 1 - -2063 
= -7937, 
log (1 - r) = ^-^ log -7937 
= - X 1-899657 
•100343 
V 
whence the value of r is readily obtained. 
I will now consider a formula for giving the number of cases at the end of 
a month in terms of the number at the beginning, the total population, the 
number of anophelines and the recovery rate. 
Let ??io be the number of cases at the beginning of the month out of a popula- 
tion p; nit the number after the t^^ bite and r the recovery rate when there are 
71 infecting bites in the month ; then 
P — VI f_-^ 
mt - vit-i -f - — — rnit-i , 
or nit = — - — ''j + 1. 
Put R for ^1— ^ — and this equation may be written 
mt = mt-iR + 1. 
Now r remains constant for the month under consideration and therefore 
also R. Hence 
m(_i = ??if_2-K + 1, 
ma = m^R + 1, 
mi = nioR + 1. 
From these equations 
1 - m 
nit = nioR'^ + ^ _ 
