Hello Thomas,

Thanks for your helpful feedback.  The model you propose is not good- it's excellent.  The following is a summary of the models I tested for this data:

                             Collinearity
Model                SC      with all parameters
---------------------------------------------
Malthus        0.5677005     NA
Verhulst       0.5677032     4.3
Richards       0.567703      15.4
Blumberg       0.05629742    20.4    (*)
Generalized    0.02591176    1495.1
2 var model    0.005744879   10.3  <-- best model

(*) This fit corresponds to a 4 parameter Blumberg model 
with K fixed according to supposition of inflexion point N_inf

Fit of Parameters

Model                r         K (maximum population)
-------------------------------------------------
Malthus        0.0197321       +oo                  (*)
Verhulst       0.01973206      89,219,750,000,000   (*)
Richards       0.01973206      394,641,100          (*)
Blumberg       1.488546e-08    64,672,787  (**)
Generalized    7.283825e-10    118,310,000 (**)
2 var model    5.021216e-02    35,805,760

(*)    The saturation point K for these models is unrealistically high. In the case of the Richards model, this saturation point would suppose a population density of 430.62 inhabitants per square kilometer, which, although possible, I would consider unsustainable for Venezuela (area of 916,445 square kilometers).
(**) Low fitted values of r are compensated by alpha values close to 2.

SC is the sum of squares weighed by std deviation goodness of fit meassure.  The proposed 2 variable model SC is 5 times lower than the Generalized model and has identifiable parameters.  Still, I have some questions regarding this 2 variable model:

(1) Could you point me to some literature (if there is any) regarding the proposed model for demographical dynamics? In there is no literature to your knowledge (and there certainly isn't to mine), how did you come up with this model?  I'm writing an academic paper on this and I really need to know who to cite. 

(2) From what I see, it is a 2 compartiment model where you call variable y1 the inactive population and y2 the active population.  I take it that "active" and "inactive" refer to concepts in the epidemological context, but what would their meaning be in a population growth census model?  "Active" as being the part of the population that is procreating offspring does not sound reasonable as an interpretation for this concept.
My guess is that maybe inactive refers to the part of the population that is living in pre-industrial conditions (in the context of the demographic transition theory).  The population then gradually shifts into a modern, urban lifestyle with lower mortality and fertility rates.  In Venezuela, there was a major malaria epidemic and economic depressions (resulting from low coffee prices which was Venezuela's main export before oil) during the 1891-1920 period. Since 1920, Venezuela became an oil-producing country and this brought about the modern age.
This is just my guess but since you proposed the model, perhaps you can clarify this point.

(3) Does this 2 variable model have an analytical solution? The analytical solution of y1 is easy enough- an exponentially decreasing function.  But the solution of y2 eludes me.  also, what would the analytical equation for the inflection point of the population be?

Again, thank you for your really valuable feedback.

Regards,

jose loreto romero palma

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