At this work, a socio-demographic dynamic generic model is presented. Some welfare variables are introduced in it. These welfare variables are defined by the UN in the Reports about Human Development (UNDP, 1990-2011).
The welfare variables are: Human Development Index (HDI), Gender Empowerment Index (GEM), Gender Development Index (GDI) and Human Poverty Index for OECD countries (HPI-2). These index are introduced as main variables and they are interrelated with demographic variables.
The mathematic model has been obtained because we have continued a constructive method. This has been divided into three steps:
Step 1, a Temporal Model has been constructed. It is different for each welfare variable. 
Step 2, a Temporal Model has been designed. The interaction of the welfare variables has been used.
Step 3, a Age-Structured Model has been formulated.
In the Step 2, two ways have been distinguished. These ways lead to two models. On the one hand, Temporal Model II, which involves three welfare variables. On the other hand, Temporal Model III, it is an extension of Temporal Model II, in which Human Poverty Index for OECD countries is added. These ways remain bifurcated in Step 3. This differentiation is made for one reason, we want to construct a generic demographic model, i.e., a model applicable to any country in the world. 
At the UN Reports (UNDP, 1990-2009), a welfare variable exists, Human Poverty Index. There are two different. if you want it for a OECD country, you’ll use IPH-2. But if you want it for a other country, you’ll use IPH-1.
Thus, this distinction should be reflected in the models of this work. The Temporal Model II and the Age-Structured Model II are to any country (these model don’t have the Human Poverty Index). Instead, The Temporal Model III and the Age-Structured Model III are to OECD countries, because the IPH-2 is inserted into them.
Note that in this work, we don’t study any model, in which the Human Poverty Index for no OECD countries is been used. Because there aren’t enough historical demographic data for these countries.
The models have been validated considering two formulations: the deterministic formulation and stochastic formulation. the methodology proposed by Caselles (1992a, 1994, 2008) has been followed. Both validations, for every one of the models, have been successful since it has been able to obtain, in the case of validation of the deterministic formulation high determination coefficient and a random residues. In the case of stochastic formulation, historical data are graphically comprised within the simulated confidence intervals for them.
The stochastic formulation has been used for the simulation of the future, because this formulation provides more information, giving an idea of the reliability of the results. For it we use Age-Structured Model II.  This simulation of the future has been made using two objectives to optimize. One is to obtain a stable demographically and the other to increase the quality of life of a country.
Finally, the welfare variables, which were updated on the UN Human Development Report (UNDP, 2010), has been presented. Namely, the Human Development Index, the Hybrid Human Development Index, the Gender Differentiation Index and the Multidimensional Poverty Index. These indices differ in calculations and meaning to the old, even though some of them have the same name as those presented in previous reports (UNDP, 1990-2009). Still, in this paper we show that these new indices can be exchanged in the Temporal Models that we defined. For the Multidimensional Poverty Index, it is impossible to validate the model proposed here, again we don’t have enough historical data about it.