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
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
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The augmented matrix is,
We have given system of linear equation is,
In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.
So, the first row is
the second row is
and the third row is
Therefore the augmented matrix for this linear system is,
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