Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Abstract

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. a b s t r a c tWe obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Padé technique. We present and discuss graphical results for our solutions.

GHM method for obtaining rationalsolutions of nonlinear differential equations

“…Moreover, the initial conditions are chosen as: n (0)=0.5045, s (0)=0.2059, c (0)=0.1559, and e (0)=0.1337, as reported in (Guerrero et al 2013). …”

Backward bifurcation in a smoking cessation model with media campaigns

“…The increasing focus of government and health care organizations on the prevention and control of addictive behaviors, such as tobacco and alcohol use have also reckoned interest of mathematical modelers in this area [9][10][11][12][13][14][15]. Smoking itself is not a disease but it attributes to many other health problems, like heart attacks, ischemic heart disease (stroke), chronic obstructive pulmonary disease, cerebrovascular disease, peripheral vascular disease, hypertension and cancer.…”

Asymmetric Solutions of SDOF System with Wire Rope Vibration Isolator Subjected to Harmonic Excitation

“…[10][11][12] HAM still works accurately when the parameters in nonlinear ODEs and PDEs are large and has been successfully applied to a wide range of nonlinear problems. [13][14][15][16][17][18][19][20][21][22][23] However, as will be shown in the present paper, the standard HAM cannot capture asymmetric periodic solutions of nonlinear ODEs or PDEs. In the present work, a technique is put forward in the frame of HAM to capture asymmetric periodic solutions of dynamic systems with wire rope isolators which exhibit asymmetric restoring force (described in detail in the next section).…”