Do Longer Delays Matter? The Effect of Prolonging Delay in CTL Activation

The activation of a specific immune response takes place in the lymphoid organs such as the spleen. We present here a simplified model of the proliferation of specific immune cells in the form of a single delay equation. We show that the system can undergo switches in stability as the delay is increased, and we interpret these results in the context of sustaining an effective immune response to a dendritic cell vaccine.Comment: 7 pages, 5 figures. Presented at the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications that took place in Dresden, Germany, May 25-28, 201

Vibrational properties characterization of mouse embryo during microinjection

To determine the vibration characteristics (natural frequencies and mode shapes) of a mouse embryo during microinjection the modal analysis is used. The spherical mouse embryo 60 μm in diameter is modeled as elastic finite elements biostructure consisting of 6μm thick micromembrane and 38 μm in diameter nucleus. Embryo modeling and modal analysis were based on the use of the finite elements method in the modal analysis system of ANSYS software. The modal analysis was carried out for first six modes of embryo natural frequencies. The numerical analysis of dependence of embryo own frequencies on the boundary conditions and external loads are presented. The relevant illustrations of the typical variations of the shape, deformation and particle velocities of vibrating embryo are given. [Projekat Ministarstva nauke Republike Srbije, br. OI174001: Dynamics of hybrid systems with complex structures: Mechanics of materials

An in-host model of HIV incorporating latent infection and viral mutation

We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is presented which characterizes the long time behavior of the model. Finally, we study the effects of an antiretroviral drug and treatment implications.Comment: 10 pages, 7 figures, Proceedings of AIMS Conference on Differential Equations and Dynamical Systems (2015

Information Geometry and Evolutionary Game Theory

The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.Comment: Added reference

Limit cycles by FEM for a one - parameter dynamical system associated to the Luo - Rudy I model

An one - parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented.Comment: Presented at the 18th Conference on Applied and Industrial Mathematics - CAIM 2010, Ia\c{s}i, Romania, October 14-17, 2010; http://www.romai.ro, http://rj.romai.r