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Modeling Adaptive Behavior in Influenza Transmission

W. Wang (2012)

Mathematical Modelling of Natural Phenomena

Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical...

Modeling the role of constant and time varying recycling delay on an ecological food chain

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2010)

Applications of Mathematics

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...

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...

Models of interactions between heterotrophic and autotrophic organisms

Urszula Foryś, Zuzanna Szymańska (2009)

Applicationes Mathematicae

We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.

Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds

Prabhakar G. Vaidya, Swarnali Majumder (2011)

Mathematica Bohemica

We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate...

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang, Alberto Cabada, Juan J. Nieto (1993)

Annales Polonici Mathematici

The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems

A. Raouf Chouikha (2005)

Applicationes Mathematicae

We first examine conditions implying monotonicity of the period function for potential systems with a center at 0 (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems ( L D , F ) for various values of the parameters D and F. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for ( L D , F ) . Our results may be viewed as a contribution to proving (or disproving) a conjecture...

Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems

A. Raouf Chouikha (2005)

Applicationes Mathematicae

We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function...

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