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Host Factors in Viral Life Cycles

G. Pérez-Vilaró, J. Jungfleisch, V. Saludes, N. Scheller, M. Giménez-Barcons, J. Díez (2012)

Mathematical Modelling of Natural Phenomena

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...

Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

G. Bocharov, V. Chereshnev, I. Gainova, S. Bazhan, B. Bachmetyev, J. Argilaguet, J. Martinez, A. Meyerhans (2012)

Mathematical Modelling of Natural Phenomena

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 matrix models and their population dynamic consequences

Sanyi Tang (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well...

Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as...

Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

Nathalie Verdiere, Lilianne Denis-Vidal, Ghislaine Joly-Blanchard, Dominique Domurado (2005)

International Journal of Applied Mathematics and Computer Science

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...

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