Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

Abstract

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems -the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

On the limiting Stokes wave of extreme height in arbitrary water depth

“…In this paper, the limiting Stokes' wave in arbitrary water depth is successfully solved by an analytic approximation method, namely the homotopy analysis method (HAM) (Liao 1992(Liao , 1999(Liao , 2003(Liao , 2009(Liao , 2010(Liao , 2012Van Gorder & Vajravelu 2008;Mastroberardino 2011;Kimiaeifar et al 2011;Vajravelu & Van Gorder 2012;Sardanyés et al 2015;Liao et al 2016;Zhong & Liao 2017, 2018Liu et al 2018a,b). Unlike perturbation methods (Schwartz 1974;Cokelet 1977), the HAM is independent of any small/large physical parameter.…”

A new non-perturbative approach in quantum mechanics for time-independent Schrödinger equations

“…Furthermore, it has been proved that even the famous Euler transform is also a special case of the HAM [12]. In this way, nearly all restrictions of perturbation methods have been overcome by the HAM, as illustrated by its users in a wide range of fields with more than thousands related publications (for examples, please see [19][20][21][22][23][24][25][26]). It should be emphasized that the HAM has been successfully applied to theoretically predict the existence of the so-called steady-steady resonant gravity waves [27], which had been later experimentally confirmed [28].…”

Non-linear thermal radiation and magnetic field effects on the flow Carreau nanofluid with convective conditions

“…The results obtained by homotopy analysis method (HAM) are preferred than the numerical solutions in perspective of the following points [31][32][33][34][35][36][37][38][39]: -The HAM gives the solutions within the domain of interest at each point while the numerical solutions hold just for discrete points in the domain. -Algebraically developed approximate solutions require less effort and having a sensible measure of precision when compared to numerical solution which are more convenient for the scientist, an engineer or an applied mathematician.…”