Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit no overt symptoms. Let r 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 3, so dy/dt = -By. (1) Suppose also that the disease spreads at a rate proportional to the product of r and y; thus dr/dt = -axy. (2) a) condition y(0) = Yo- Determine the proportion of carriers in the population at any time t, subject to the initial

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Some diseases (such as typhoid fever) are spread largely by carriers, individuals who
can transmit the disease but who exhibit no overt symptoms. Let r 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 3, so
dy/dt = -By.
(1)
Suppose also that the disease spreads at a rate proportional to the product of a and y; thus
dx/dt = -axy.
(2)
a)
condition y(0) = Yo-
Determine the proportion of carriers in the population at any time t, subject to the initial
Transcribed Image Text:Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit no overt symptoms. Let r 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 3, so dy/dt = -By. (1) Suppose also that the disease spreads at a rate proportional to the product of a and y; thus dx/dt = -axy. (2) a) condition y(0) = Yo- Determine the proportion of carriers in the population at any time t, subject to the initial
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