Abstract.

In this paper we obtain approximated analytical solutions for a mathematical model for the cocaine consumption in Spain using the Homotopy Analysis Method. The interest of the model is that, based on real data from Spanish Statistical Institute, it has been used to explain successfully the real evolution of the epidemic in Spain [18, 19]. First, we obtain with HAM an analytical approximation to the real solution of the model in the form of a power series of the time t. Second, we enlarge its domain of convergence applying the Pade after-treatment to the HAM solution.

Keywords:

dynamic model, epidemic model; Homotopy analysis method, Homotopy-Pade tech- nique, multistage homotopy analysis method, cocaine consumption model.