In this paper, we derive a variant of the classical Keller–Segel model chemotaxis incorporating growth term logistic type for cell population , say with and nonstandard chemical production–degradation mechanism involving first- second-order derivatives logarithm density, via ()-hydrodynamical system associated modified Ginzburg–Landau equation governing evolution complex wavefunction . chemotac...

We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells,...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of ...

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent 0 < α ≤ 2. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when α < 1 and the initial confi...

A Primer on Mathematical Models in Biology Lee A. Segel and Leah Edelstein-Keshet This textbook grew out of a course that the popular and highly respected applied mathematician Lee Segel taught. It introduces differential equations, biological applications, and simulations and emphasizes molecular events, excitable systems, and small protein and genetic circuits. It is intended for upper-level ...

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models describe phenomenon are celebrated Keller–Segel equation chemotaxis kinetic equation. These two equations organism’s at macro- mesoscopic level, respectively, asymptotically equivalent parabolic regime. The way which organism respo...

This paper has applied a hybrid method called the homotopy perturbation transformation technique to solve fractional-order Newell-Whitehead-Segel equations. First, we used Yang given problem, and then, was implemented complete procedure of suggested method. The proposed is simplified requires small calculation achieve solution targeted problem. Moreover, derived results are in close contact wit...

A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a new entropy functional yielding gradient estimates for the cell density and chemical concentration. The main features of the numerical scheme are positivity p...

Cigarette smoking is a major cause of death worldwide resulting in over six million deaths per year. Cigarette smoke contains complex mixtures of chemicals that are harmful to nearly all organs of the human body, especially the lungs. Cigarette smoking is considered the major risk factor for many lung diseases, particularly chronic obstructive pulmonary diseases (COPD) and lung cancer. However,...