# Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel

M. Neamţu; L. Buliga; F. R. Horhat; D. Opriş

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 1, page 44-61
- ISSN: 0973-5348

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topNeamţu, M., et al. "Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel." Mathematical Modelling of Natural Phenomena 2.1 (2010): 44-61. <http://eudml.org/doc/222214>.

@article{Neamţu2010,

abstract = {
The aim of this paper is to study the steady states of the mathematical models with delay
kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical
models of infectious diseases it is important to predict whether the infection disappears
or the pathogens persist. The delay kernel is described by the memory function that reflects the
influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and
normated function k defined on [ 0, ∞ ). By using the coefficient of the kernel k,
as a bifurcationparameter, the models are found to undergo a sequence of Hopf bifurcation.
The direction and the stability criteria of bifurcation periodic solutions are obtained by applying
the normal form theory and the center manifold theorems. Some numerical simulation examples for
justifying the theoretical results are also given.
},

author = {Neamţu, M., Buliga, L., Horhat, F. R., Opriş, D.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {delay differential equation; stability; Hopf bifurcation; pathogen-immune interaction},

language = {eng},

month = {3},

number = {1},

pages = {44-61},

publisher = {EDP Sciences},

title = {Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel},

url = {http://eudml.org/doc/222214},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Neamţu, M.

AU - Buliga, L.

AU - Horhat, F. R.

AU - Opriş, D.

TI - Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 2

IS - 1

SP - 44

EP - 61

AB -
The aim of this paper is to study the steady states of the mathematical models with delay
kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical
models of infectious diseases it is important to predict whether the infection disappears
or the pathogens persist. The delay kernel is described by the memory function that reflects the
influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and
normated function k defined on [ 0, ∞ ). By using the coefficient of the kernel k,
as a bifurcationparameter, the models are found to undergo a sequence of Hopf bifurcation.
The direction and the stability criteria of bifurcation periodic solutions are obtained by applying
the normal form theory and the center manifold theorems. Some numerical simulation examples for
justifying the theoretical results are also given.

LA - eng

KW - delay differential equation; stability; Hopf bifurcation; pathogen-immune interaction

UR - http://eudml.org/doc/222214

ER -

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