## Solution Of Ode Models

The solution at epidemic equilibrium of the simple set of equations on page 171 be arrived at analytically by noting that under equilibrium the values of the state variables remain constant so that therefore the rates of change of these variables (the differentials) become zero. From this fact we have dX dt

Thus at equilibrium

and from this set of equations expressions can be derived for the values for the state variables at equilibrium in terms of the parameters:

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