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Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

Xiangdong Zhao (2024)

Czechoslovak Mathematical Journal

We study the chemotaxis system with singular sensitivity and logistic-type source: u t = Δ u - χ ∇ · ( u ∇ v / v ) + r u - μ u k , 0 = Δ v - v + u under the non-flux boundary conditions in a smooth bounded domain Ω ⊂ ℝ n , χ , r , μ > 0 , k > 1 and n ≥ 1 . It is shown with k ∈ ( 1 , 2 ) that the system possesses a global generalized solution for n ≥ 2 which is bounded when χ > 0 is suitably small related to r > 0 and the initial datum is properly small, and a global bounded classical solution for n = 1 .

Global stability analysis and control of leptospirosis

Kazeem Oare Okosun, M. Mukamuri, Daniel Oluwole Makinde (2016)

Open Mathematics

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction...

Global stability of steady solutions for a model in virus dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2003)

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

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 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...

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 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.

Currently displaying 761 – 780 of 1850