Question

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 = −βy. Suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx/dt = −αxy. 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

Answer 1

Answer:

The detailed derivation is shown in the attachment

Step-by-step explanation:

The step by step explanation is as shown in the attachment.

Basically, what was applied is the knowledge of differentiation and integration.