19 research outputs found
Differential transformation method (DTM) for solving SIS and SI epidemic models
In this paper, the differential transformation method (DTM) is employed to find the semi-analytical solutions of SIS and SI epidemic models for constant population. Firstly, the theoretical background of DTM is studied and followed by constructing the solutions of SIS and SI epidemic models. Furthermore, the convergence analysis of DTM is proven by proposing two theorems. Finally, numerical computations are made and compared with the exact solutions. From the numerical results, the solutions produced by DTM approach the exact solutions which agreed with the proposed theorems. It can be seen that the DTM is an alternative technique to be considered in solving many practical problems involving differential equations
Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach
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
Analytic Comparison of Some Epidemic Models with Vaccination
AbstractIn this paper, we discuss the elementary properties of some simple SI, SR, SIR and SEIR epidemic models whose parameterizing functions (such as per-capita death rate, disease transmission, removal rate etc.) might be eventually time-varying but nonnecessarily time-integrable. Vaccination rules based of feedback, measuring the numbers of some of the partial populations defining the disease progress, are also discussed
Solving a model for the evolution of smoking habit in Spain with homotopy analysis method
We 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.
©Guerrero, F.; Santonja, F.; Villanueva Micó, RJ. (2013). Solving a model for the evolution of smoking habit in Spain with homotopy analysis method. Nonlinear Analysis: Real World Applications. 14(1):549-558. doi:10.1016/j.nonrwa.2012.07.015S54955814