Hopf bifurcation of a mathematical model for growth of tumors with an action of inhibitor and two time delays.
Horseshoe in a class of planar mappings.
Host Factors in Viral Life Cycles
Viruses are obligate intracellular parasites that rely on the host cell for expansion. With the development of global analyses techniques like transcriptomics, proteomics and siRNA library screening of complete cellular gene sets, a large range of host cell factors have been discovered that either support or restrict virus growth. Here we summarize some of the recent findings and focus our discussion on the hepatitis C virus and the human immunodeficiency...
Hotelling test for highly correlated data
How and why do neurons generate complex rhythms with various frequencies?
How hyperpolarization and the recovery of excitability affect propagation through a virtual anode in the heart.
Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling
HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii)...
Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics.
Hydrodynamic flow between rotating eccentric cylinders with suction at the porous walls.
Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor
The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it...
Identification d'un phénomène bactériologique
Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology.
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model.
Immune responses against conserved and variable viral epitopes.
Immune responses and viral phenotype: Do replication rate and cytopathogenicity influence virus load?
Immunological barrier for infectious diseases
A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.
Immunotherapy with interleukin-2: A study based on mathematical modeling
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation
Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn...
Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis
Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin...
Improving EWMA plans for detecting unusual increases in Poisson counts.