Age-structured mathematical modeling approach to short-term diffusion of electronic commerce in Spain

The dynamics over the next few years of the Spanish mobile telecommunications market share: a mathematical modelling approach

“…Mathematical models are powerful tools to explain and predict the process of adoption of a new product or innovation over time and to attract new ones [5][6][7][8]. In this case, taking into account official data from CMT (Spanish Telecommunications Market Commission) [4], the Spanish mobile telecommunications market is divided into five main groups: Movistar-Telefonica, Vodafone, Orange, Yoigo and MVO (others Mobile Virtual Operators).…”

Computational Modeling With Uncertainty of Frequent Users of E-Commerce in Spain Using an Age-Group Dynamic Nonlinear Model With Varying Size Population

“…As we have pointed out in the Introduction, in our previous contribution [7] we proposed a deterministic mathematical model to describe the dynamics of EC in Spain, where the above six age groups were considered. In the present paper, our aim is to treat the uncertainty included in the sampled data.…”

“…In the present paper, our aim is to treat the uncertainty included in the sampled data. Thus, the idea of considering all the age groups could make the random model very complex, as it occurs in [7]. Therefore, taking into account the significant difference between the percentage of frequent users of EC if they are younger or older than 45 years old, we are going to consider the age groups 15-44 and 45-74.…”

“…In [7], the age, the innovators and the imitators have been considered in the model. Nevertheless the uncertainty of the data coming from a survey, and consequently, with an intrinsic error that may influence the study, has not been considered and treated.…”

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

“…These interesting studies include a qualitative equilibrium analysis and numerical simulations of the competition dynamics. In [11] some of the authors of the present paper proposed an age-structured compartmental mathematical model (similar to the ones used to model epidemics [12]) to describe the dynamics of e-commerce using real data from the Spanish National Statistical Institute (INE). This study is performed by combining two mathematical models, the first one is a demographic model providing certain demographic parameters required in the formulation of the second model, which is addressed to describe the diffusion of e-commerce.…”