# Irina BadralexiPolytechnic University of Bucharest | UPB · Department of Mathematics

Irina Badralexi

PhD

## About

12

Publications

13,454

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16

Citations

Citations since 2017

## Publications

Publications (12)

In this paper, we study two mathematical models, involving delay differential equations, which describe the processes of erythropoiesis and leukopoiesis in the case of maintenance therapy for acute lymphoblastic leukemia. All types of possible equilibrium points were determined, and their stability was analyzed. For some of the equilibrium points,...

In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment consider...

We introduce a mathematical model which captures the cellular evolution in the case of patients diagnosed with acute lymphoblastic leukemia and who are under maintenance therapy. We develop the model using a system of delay-differential equations. The main goal of this paper is to describe the complex biological model by considering three different...

The model studied in this paper describes the competitive interaction between healthy and malignant cells in leukemia with the involvement of the immune system. The model consists of 9 delay-differential equations with 9 delays. Local stability is investigated for the equilibrium points of the system. Lyapunov-Krasovskii functionals related

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (Mean First Passage Time). We study different biologically relev...

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time). We study different biologically relev...

The complex model of cells evolution in leukemia considers the competition between the populations of healthy and leukemic cells, the asym- metric division and the immune system's action in response to the disease. Delay differential equations are used to describe the dynamics of healthy and leukemic cells in case of CML (Chronic Myeloid Leukemia)....

We capture the evolution in competition of healthy and leukemic cells in Chronic Myelogenous Leukemia (CML) taking into consideration the response of the immune system. Delay-differential equations in a Mackey-Glass approach are used. We start with the study of stability of the equilibrium points of the system. Conditions on parameters for the loca...

The complex model studied in this paper considers the competition between the populations of healthy and leukemic stem-like short-term and mature leukocytes and the influence of the T-lymphocytes on the evolution of leukemia. Delay differential equations with delay-dependent parameters are used in a modified Mackey-Glass approach, with the consider...

This paper introduces a complex model that describes the competition between the populations of healthy and leukemic cells and the inuence of the T-lymphocytes on the evolution of leukemia. The system consists of 5 delay differential equations derived from a Mackey-Glass approach. The main results of this work center around suffcient linear stabili...

Iteration methods are very useful in solving nonlinear algebraic equations. The most famous such method is Newton’s method deduced by first order Taylor expansion. In 2003, J. H. He gives a new faster convergent method, based on second order Taylor expansion, that gives a quadratic equation for the iterations difference xn+1-xn . However He’s metho...

Recent versions of the well-known Newton-Raphson method for solving algebraic equations are presented. First of these is the method given by J. H. He in 2003. He reduces the problem to solving a second degree polynomial equation. However He’s method is not applicable when this equation has complex roots. In 2008, D. Wei, J. Wu and M. Mei eliminated...