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kirza4 [7]
3 years ago
14

Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit n

o 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

Mathematics
1 answer:
Margaret [11]3 years ago
6 0

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.

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