# Immunological barrier for infectious diseases

Applicationes Mathematicae (1997)

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

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topBarradas, 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

top- [1] G. Bell, Prey-predator equations simulating an immune response, Math. Biosci. 16 (1973), 291-314. Zbl0253.92003
- [2] G. Bell, A. Perelson and G. Pimbley, Theoretical Immunology, Marcel Dekker, New York, 1978. Zbl0376.92001
- [3] C. Bruni, Immune response: a system approach, in: Theoretical Immunology, Marcel Dekker, New York, 1978, 379-414.
- [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] G. I. Marchuk, Mathematical Models in Immunology, Transl. Ser. in Math. Engineering, Optimization Software, Inc., Publ. Division, New York, 1983. Zbl0556.92006
- [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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