Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit no overt symptoms. Let x and y, respectively, denote the proportion of susceptibles and carriers in the population.
Suppose that carriers are identified and removed from the population at a rate B, so
dy/dt=-By. Suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx/dt=-axy.

a) Determine y at tany time t by solving eq(i) subject to the initial condition y(0)=y0
b) Use the result of part (a) to find x at any time t by solving Eq.(ii) subject to the initial condition x(0)=x0
c) Find the proportion of the population that escapes the epidemic by finding the limiting value of x as t approaches infinity