Displaying similar documents to “An epidemic model with a time delay in transmission”

Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation...

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

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2010)

Applications of Mathematics

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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...

The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response

Radouane Yafia (2009)

Applicationes Mathematicae

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We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses...

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

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The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties...

Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models

Xiao Wang, Zhixiang Li (2007)

Open Mathematics

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In this paper, we discuss the special diffusive hematopoiesis model ∂ P ( t , x ) ∂ t = Δ P ( t , x ) - γ P ( t , x ) + β P ( t - τ , x ) 1 + P n ( t - τ , x ) with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.