semi-analytical ‎m‎ethod to solve the non-linear system of equations to model of evolution for smoking habit in ‎spain

An epidemiological model of smoking habit is studied by using one of flexible and accurate semianalytical methods. for this reason, the homotopy analysis transform method (hatm) is applied. convergence theorem is studied and several hcurves are demonstrated to show the convergence regions. also, the optimal convergence regions are obtained by demonstrating the residual error functions versus h. the numerical tables are presented to show the precision of method.