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Polymerization of proteins is a biochemical process involved in different diseases.
Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In
this paper we consider a general polymerization model and propose a high-order numerical
scheme to investigate the behavior of the solution. An important property of the equation
is the mass conservation. The WENO scheme is built to preserve the total mass of proteins
along time....
Recently the effect of a quiescent phase (or dormant/resting phase in applications) on
the dynamics of a system of differential equations has been investigated, in particular with respect
to stability properties of stationary points. It has been shown that there is a general phenomenon
of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for
homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower
dynamics. We show that...
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...
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