# Determining If the 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

dI/dt=aH-(b+c)I

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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