IJPAM: Volume 117, No. 2 (2017)

Title

ANALYSIS OF A MATHEMATICAL MODEL OF ADAPTIVE
IMMUNE RESPONSE TO VIRUS INFECTION

Authors

Anka Markovska
Department of Electrical Engineering, Electronics and Automatics
Faculty of Engineering
South-West University ``Neofit Rilski", 66, Ivan Mihailov Str.,
Blagoevgrad, 2700, BULGARIA

Abstract

A mathematical model of adaptive immune response to a viral infection is formulated by five nonlinear ordinary differential equations. The model describes the interactions between a virus, uninfected cells, infected cells, and the adaptive immune response represented by the antibodies and cytotoxic T lymphocytes. Theorems of existence, uniqueness and non-negativity of solution are proven. Numerical simulations of the model are presented.

History

Received: 2017-06-14
Revised: 2017-11-15
Published: December 23, 2017

AMS Classification, Key Words

AMS Subject Classification: 03H10
Key Words and Phrases: mathematical model, ordinary differential equations, numerical simulations

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Bibliography

1
A. Abbas, Lichtman, A., Basic Immunology: Functions and Disorders of the Immune System. Elsevier, Philadelphia, (2009).

2
P. Hartman, Ordinary Differential Equations. John Wiley and Sons, New York-London-Sydney (1994).

3
G.Marchuk, Some mathematical models in immunology, Proc. of the IFfP Conference on Optimization Techniques. Heidelberg: Springer-Verlag,(1978), P.'41- 62.

4
A. Markovska, Mathematical Model of Humoral Immune Response to Viral Infection, International Journal of Modern Sciences and Engineering Technology, V.3 Issu2,(2016), pp 46-52.

5
A. Markovska, On a Mathematical Model Describing the Adaptive Immune Response to Viral Infection, Mathematics and natural sciences, Blagoevgrad, Bulgaria, vol. 1(2015) pp. 80-85.

6
L. Shampine, M.W. Reichelt,The Matlab ODE suite, SIAM J. Sci. Comput. 18,(1997), P. 1-22.

7
D. Wodarz, Killer Cell Dynamics, Springer, New York, Berlin, (2006).

How to Cite?

DOI: 10.12732/ijpam.v117i2.1 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 2
Pages: 255 - 261


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