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

Over the last few years electronic commerce, e-commerce for short, has become one of the most accepted purchasing systems this having became the easiest way of accessing a large variety of goods. E-commerce provides: the possibility of comparing costs and bids without going to outlets and therefore, saving time and money; the availability of detailed characteristics of goods; the possibility of acquiring new goods available abroad. Moreover, the form of payments are getting progressively safer and more reliable on the Internet. In this paper we develop a mathematical model to study future short-term trends of e-commerce in Spain. To do this, we divide the total population into age groups and each age group into two subgroups: the first one consists of people adopting this technology and the second one who do not. Then, we consider a nonlinear diffusion model whose parameters are the innovation coefficients associated with each age group and related to advertising, and the imitation coefficients related to the influence of an adopting technology group on non-adopting group. These parameters are estimated by fitting the available real data from the Spanish Statistic Institute. Finally, an analysis of statistic sensitivity is included.