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Global Stability of Steady Solutions for a Model in Virus Dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

Global stability, periodic solutions, and optimal control in a nonlinear differential delay model.

Ivanov, Anatoli F., Mammadov, Musa A. (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy.

Smieja, Jaroslaw, Swierniak, Andrzej, Duda, Zdzislaw (2000)

Journal of Theoretical Medicine

Graph pattern analysis with PatternGravisto.

Klukas, Christian, Koschützki, Dirk, Schreiber, Falk (2005)

Journal of Graph Algorithms and Applications

Gravitational collapse of a Brownian gas

Clément Sire, Pierre-Henri Chavanis (2004)

Banach Center Publications

We investigate a model describing the dynamics of a gas of self-gravitating Brownian particles. This model can also have applications for the chemotaxis of bacterial populations. We focus here on the collapse phase obtained at sufficiently low temperature/energy and on the post-collapse regime following the singular time where the central density diverges. Several analytical results are illustrated by numerical simulations.

Growth model with migration: structure of optimal saving rates

Robert Kruszewski (2006)

Banach Center Publications

Growth of heterotrophe and autotrophe populations in an isolated terrestrial environment

Piotr Paweł Szopa, Monika Joanna Piotrowska (2011)

Applicationes Mathematicae

We consider the model, proposed by Dawidowicz and Zalasiński, describing the interactions between the heterotrophic and autotrophic organisms coexisting in a terrestrial environment with available oxygen. We modify this model by assuming intraspecific competition between heterotrophic organisms. Moreover, we introduce a diffusion of both types of organisms and oxygen. The basic properties of the extended model are examined and illustrated by numerical simulations.