Assume that the number of immune cells is constant at density B0. The dynamics of the virus are then given by the ordinary differential equation, dM dt =rM1−M K−βMB0, where r,K and β are positive constants, and B0 is also constant. (a) Give biological meanings for each of the parameters r,K and β. (b) Taking the non-dimensional variables η = M K [3] , and τ = rt, derive the non-dimensionalised system, dn dτ =η(−η), where c is a constant and stating how the non-dimensional parameter is defined in terms of r,B0 and β. [7] (c) Hence find a condition on the parameter β for the cells to successfully eradicate the virus. [
Assume that the number of immune cells is constant at density B0. The dynamics of the virus are then given by the ordinary differential equation, dM dt =rM1−M K−βMB0, where r,K and β are positive constants, and B0 is also constant. (a) Give biological meanings for each of the parameters r,K and β. (b) Taking the non-dimensional variables η = M K [3] , and τ = rt, derive the non-dimensionalised system, dn dτ =η(−η), where c is a constant and stating how the non-dimensional parameter is defined in terms of r,B0 and β. [7] (c) Hence find a condition on the parameter β for the cells to successfully eradicate the virus. [
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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Assume that the number of immune cells is constant at density B0. The dynamics of the virus are then given by the ordinary differential equation, dM dt =rM1−M K−βMB0, where r,K and β are positive constants, and B0 is also constant. (a) Give biological meanings for each of the parameters r,K and β. (b) Taking the non-dimensional variables η = M K [3] , and τ = rt, derive the non-dimensionalised system, dn dτ =η(−η), where c is a constant and stating how the non-dimensional parameter is defined in terms of r,B0 and β. [7] (c) Hence find a condition on the parameter β for the cells to successfully eradicate the virus. [
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