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Chemotactic bacteria are known to collectively migrate towards sources of attractants. In confined convectionless geometries, concentration "waves" of swimming Escherichia coli can form and propagate through a self-organized process involving hundreds of thousands of these microorganisms. These waves are observed in particular in microcapillaries or(More)
We consider a model for the polymerization (fragmentation) process involved in infectious prion self-replication and study both its dynamics and non-zero steady state. We address several issues. Firstly, we extend a previous study of the nucleated polymerization model [M.L. Greer, L. Pujo-Menjouet, G.F. Webb, A mathematical analysis of the dynamics of prion(More)
Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical(More)
OBJECTIVES We evaluated the parameters influencing CD4 cell reconstitution after the introduction of highly active antiretroviral therapies in real life, as well as the frequency and the determinants of the discrepancies occurring between virus and CD4 cell count evolution. DESIGN AND METHODS A total of 317 pre-treated patients starting a protease(More)
We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions. Résumé Effets de(More)
Models for the polymerization process involved in prion self-replication are well-established and studied [H. Engler, J. Pruss, and G.F. Webb, Analysis of a model for the dynamics of prions II, J. Math. Anal. Appl. 324 (2006), pp. 98-117; M.L. Greer, L. Pujo-Menjouet, and G.F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoret.(More)
OBJECTIVES Mutations usually associated with zidovudine exposure have been observed in zidovudine-naive patients treated by stavudine in combination. These mutations were named thymidine analogue mutations (TAMs). This fact, combined with phenotypical and biochemical findings provided additional evidence for cross-resistance between zidovudine and(More)
We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasser-stein distance. The rate of convergence towards self-similarity does not degenerate as we approach the(More)
CONTEXT In the Trilège trial, following induction with a zidovudine, lamivudine, and indinavir regimen, human immunodeficiency virus (HIV) replication was less suppressed by 2-drug maintenance therapy than by triple-drug therapy. OBJECTIVE To identify mechanisms of virologic failure in the 3 arms of the Trilège trial. DESIGN Case-control study conducted(More)