Nonlinear differential equations have applications in the modelling area for a broad variety of phenomena
and physical processes; having applications for all areas in science and engineering. At the present
time, the homotopy perturbation method (HPM) is amply used to solve in an approximate or exact manner
such nonlinear differential equations. This method has found wide acceptance for its versatility and ease
of use. The origin of the HPM is found in the coupling of homotopy methods with perturbation
methods. Homotopy methods are a well established research area with applications, in particular, an applied
branch of such methods are the homotopy continuation methods, which are employed on the numerical
solution of nonlinear algebraic equation systems. Therefore, this paper presents two modified versions of
standard HPM method inspired in homotopy continuation methods. Both modified HPMs deal
with nonlinearities distribution of the nonlinear differential equation. Besides, we will use a calcium-induced
calcium released mechanism model as study case to test the proposed techniques. Finally, results
will be discussed and possible research lines will be proposed using this work as a starting point
