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Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.

Global exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure

Chaouki Aouiti, Hediene Jallouli, Mohsen Miraoui (2022)

Applications of Mathematics

We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a ( μ , ν ) -pseudo almost automorphic solution. The...

Global minimizers for axisymmetric multiphase membranes

Rustum Choksi, Marco Morandotti, Marco Veneroni (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...

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 Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

Ramalingam Sriraman, Asha Nedunchezhiyan (2022)

Kybernetika

In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the n -dimensional Clifford-valued neural network into 2 m n -dimensional real-valued counterparts in order to solve the noncommutativity...

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.

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