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 denote the proportions of susceptibles and carriers, respectively, in the population. suppose that carriers are identified and removed from the population at a rate β, so dy dt = −β y. (23) suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx dt = −αxy. (24) a. determine y at any time t by solving equation (23) subject to the initial condition y(0) = y0. b. use the result of part a to find x at any time t by solving equation (24) subject to the initial condition x(0) = x0.