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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.