Immunological barrier for infectious diseases

I. Barradas

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 289-297
  • ISSN: 1233-7234

Abstract

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A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.

How to cite

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Barradas, I.. "Immunological barrier for infectious diseases." Applicationes Mathematicae 24.3 (1997): 289-297. <http://eudml.org/doc/219170>.

@article{Barradas1997,
abstract = {A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.},
author = {Barradas, I.},
journal = {Applicationes Mathematicae},
keywords = {distributed delay; reaction of a human organism; attraction basin; immunological barrier},
language = {eng},
number = {3},
pages = {289-297},
title = {Immunological barrier for infectious diseases},
url = {http://eudml.org/doc/219170},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Barradas, I.
TI - Immunological barrier for infectious diseases
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 289
EP - 297
AB - A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.
LA - eng
KW - distributed delay; reaction of a human organism; attraction basin; immunological barrier
UR - http://eudml.org/doc/219170
ER -

References

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  1. [1] G. Bell, Prey-predator equations simulating an immune response, Math. Biosci. 16 (1973), 291-314. Zbl0253.92003
  2. [2] G. Bell, A. Perelson and G. Pimbley, Theoretical Immunology, Marcel Dekker, New York, 1978. Zbl0376.92001
  3. [3] C. Bruni, Immune response: a system approach, in: Theoretical Immunology, Marcel Dekker, New York, 1978, 379-414. 
  4. [4] H. Freedman and J. A. Gatica, A threshold model simulating humoral immune response to replicating antigens, Math. Biosci. 37 (1977), 113-134. Zbl0365.92006
  5. [5] G. I. Marchuk, Mathematical Models in Immunology, Transl. Ser. in Math. Engineering, Optimization Software, Inc., Publ. Division, New York, 1983. Zbl0556.92006
  6. [6] O. A. Smirnova, Mathematical model of immunological response, Vestnik Moskov. Univ. Ser. Fiz. Astronom. 1975 (4), 32-49 (in Russian). 

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