Inhibited population growth versus disease growth The rate population growth within a contained system is proportional to the current population y and the distance between y and the limit capacity L.  The ODE is given by : 
$\frac{dy}{dx}$ = ky ( 1 - $\frac{y}{L}$)
The rate of disease growth within a population L is proportional to those already infected y and those not yet infected (L-y).  This ODE is given by:
$\frac{dy}{dx}$ = ky (L - y)
What is the intuitive difference between the 2 equations?  
The rate of growth of each both tend to zero as the population tends to the respective limit, but how does the approach behaviour differ between the two?

Hint: if you rewrite the first equation as
$$\frac{dy}{dx} = \frac {ky}  {L} (L-y)$$
you can see that the difference with the second equation reduces to a constant in the RHS.
