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Determining If the Model is Realistic

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The solution determines if the given model is realistic.

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The governing equation for the rate at which the number healthy people changes is
dH/dt= -aH+bI
-aH because those are the ones getting sick and bI because those are the ones recovering, reverting to a healthy status.
The governing equation for the rate at which the number of infected people increases is
aH is the rate at which people get infected, bI are those getting better (thus the minus sign) and cI are those dying (they cannot get sick).
This is a set of linear differential equations and we can write it in matrix form as:
dy/dt=A y
Which we can write this as
[?(H ?@I ? )]= [?(-a&b@a&-(b+c))][?(H@I)]
The solution is of the form:
y(t)= C_1 v_1 e^(?_1 t)+C_2 v_2 e^(?_2 t)
Where C is a constant, ? is the eigenvalue of the matrix A and v is the corresponding eigenvector.
To find the eigenvalues we do the following:
det?(A-?I)= 0
Thus, ...

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