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Modeling the Cancer Stem Cell Hypothesis

C. Calmelet, A. Prokop, J. Mensah, L. J. McCawley, P. S. Crooke (2010)

Mathematical Modelling of Natural Phenomena

Solid tumors and hematological cancers contain small population of tumor cells that are believed to play a critical role in the development and progression of the disease. These cells, named Cancer Stem Cells (CSCs), have been found in leukemia, myeloma, breast, prostate, pancreas, colon, brain and lung cancers. It is also thought that CSCs drive the metastatic spread of cancer. The CSC compartment features a specific and phenotypically defined cell...

Modelling the spiders ballooning effect on the vineyard ecology

E. Venturino, M. Isaia, F. Bona, E. Issoglio, V. Triolo, G. Badino (2010)

Mathematical Modelling of Natural Phenomena

We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.

Modelling Tuberculosis and Hepatitis B Co-infections

S. Bowong, J. Kurths (2010)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...

Modular dynamical systems on networks

Lee DeVille, Eugene Lerman (2015)

Journal of the European Mathematical Society

We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations,...

Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case

Nico M. van Dijk, Karel Sladký (2006)

Kybernetika

In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as generalization of the pure stochastic case, for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II. In the present Part I it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly...

Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Noémi Nagy, Péter Simon (2013)

Open Mathematics

Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic...

Motion with friction of a heavy particle on a manifold - applications to optimization

Alexandre Cabot (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Let Φ : H → R be a C2 function on a real Hilbert space and ∑ ⊂ H x R the manifold defined by ∑ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g>0), the reaction force and the friction force ( γ > 0 is the friction parameter). For any initial conditions at time t=0, we prove the existence of a trajectory x(.) defined on R+. We are then interested in the asymptotic behaviour of...

Motion with friction of a heavy particle on a manifold. Applications to optimization

Alexandre Cabot (2002)

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

Let Φ : H be a 𝒞 2 function on a real Hilbert space and Σ H × the manifold defined by Σ : = Graph ( Φ ) . We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g > 0 ), the reaction force and the friction force ( γ > 0 is the friction parameter). For any initial conditions at time t = 0 , we prove the existence of a trajectory x ( . ) defined on + . We are then interested in the asymptotic behaviour of the trajectories when t + . More precisely,...

Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics

Luca Biasco, Luigi Chierchia (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The classical D’Alembert Hamiltonian model for a rotational oblate planet revolving near a «day-year» resonance around a fixed star on a Keplerian ellipse is considered. Notwithstanding the strong degeneracies of the model, stability results a là Nekhoroshev (i.e. for times which are exponentially long in the perturbative parameters) for the angular momentum of the planet hold.

Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. Chepyzhov, M. I. Vishik (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g ( x , t ) . We assume that g ( x , t ) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g ( x , t ) is a quasiperiodic function with respect to t , then the attractor is a continuous image of a torus. Moreover the...

Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. Chepyzhov, M. I. Vishik (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g(x,t). We assume that g(x,t) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g(x,t) is a quasiperiodic function with respect to t, then the attractor is a continuous image...

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