(b) A disease with classes S, I and Ris represented by the following system of differential...

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(b) A disease with classes S, I and Ris represented by the following system of differential equations ds = -BSI + yR, dt dI = BS I – ul, (4) - dt dR = µl – yR, dt where B, y andu are positive parameters. (i) Show that the total population N = S +I+Ris constant and use it to eliminate the equation for R. [3 marks] (ii) Use the rescalings s = S/N, i = I]N, T = BNt, c = H/(BN) and d = y/(BN) to %3D non-dimensionalise this model. [6 marks] (b) A disease with classes S, I and Ris represented by the following system of differential equations ds = -BSI + yR, dt dI = BS I – ul, (4) - dt dR = µl – yR, dt where B, y andu are positive parameters. (i) Show that the total population N = S +I+Ris constant and use it to eliminate the equation for R. [3 marks] (ii) Use the rescalings s = S/N, i = I]N, T = BNt, c = H/(BN) and d = y/(BN) to %3D non-dimensionalise this model. [6 marks]

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