STRUGGLE FROM VIEWPOINT OF MATHEMATICIANS 29 



M l = mosquito mortality, i.e., death rate per head per unit of 

 time. 

 t = time. 



If a single mosquito bites a human being on an average b l times 

 per unit of time, then the f x z x infective mosquitoes will place b l p-z l in- 

 fective bites on human beings per unit of time. If the number of 

 people not infected with malaria is (p — z), than taken in a relative 



form as it will show the relative number of healthy people in the 



total number of individuals of a given locality. Therefore, out of a 

 total number of infective bites, equal per unit of time to fr^/V, a 



definite fraction equal to - falls to the lot of healthy people, and 



the number of infective bites of healthy people per unit of time will 

 be equal to: 



& i/i 2 iP_=Li (2) 



V 



If every infective bite upon a healthy person leads to sickness, 

 then the expression (2) will show directly the number of new infec- 

 tions per unit of time, which we can put in the second place of the first 

 line of the equations (1). By analogous reasoning it follows that if 

 every person is bitten on an average b times per unit of time, the total 

 number of infective people fz will be bitten bfz times, and a fraction 



- — - — of these bites will be made by healthy mosquitoes which will 



thus become infected. Consequently the number of new infections 

 among mosquitoes per unit of time will be : 



bfz t^L? (3) 



V 1 



Now, evidently, the total number of mosquito bites on human 

 beings per unit of time will constitute a certain fixed value, which can 

 be written either as ¥p l , i.e., the product of the number of mosquitoes 

 by the number of bites made by each mosquito per unit of time, or 

 as bp, i.e., the number of persons multiplied by the number of times 



