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(ii) Use the rescalings s = S/N, i = I/N, t = BN1, c = µ/(BN) and d = y/(BN) to non-dimensionalise this model. %3D

(ii) Use the rescalings s = S/N, i = I/N, t = BN1, c = µ/(BN) and d = y/(BN) to non-dimensionalise this model. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(ii) Use the rescalings s S/N, i = I|N, T = BNt, c = µ/(BN) and d = y/(BN) to %3D non-dimensionalise this model. (iii) Calculate the steady states of the non-dimensionalised model derived in part (ii) and their stability. What are the conditions for the disease to die out?
Transcribed Image Text:(ii) Use the rescalings s S/N, i = I|N, T = BNt, c = µ/(BN) and d = y/(BN) to %3D non-dimensionalise this model. (iii) Calculate the steady states of the non-dimensionalised model derived in part (ii) and their stability. What are the conditions for the disease to die out?
(b) A disease with classes S, I and R is represented by the following system of differential equations ds = -BSI + yR, dt dI - BSI - μΙ, (4) %3! dt dR = µl – yR, dt where B, y and µ are positive parameters.
Transcribed Image Text:(b) A disease with classes S, I and R is represented by the following system of differential equations ds = -BSI + yR, dt dI - BSI - μΙ, (4) %3! dt dR = µl – yR, dt where B, y and µ are positive parameters.
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