A Mathematical Analysis for the Dynamics of Multiple Languages

In many regions of the world, languages coexist in daily life, but often one tongue increases its use at the expense of another. In the present paper, we build a large compartmental system of differential equations that meets the situation of two “prestigious” tongues and many local languages, whose use is reduced by social interaction. The focus is on the preferred language in social relationships for communicating, rather than mere knowledge. We aim at stating and proving theorems on the qualitative behavior of the system. Numerical simulations illustrate the results, giving rise to distinct dynamics.