IJPAM: Volume 117, No. 2 (2017)

Title

ON MATHEMATICAL MODELING OF THE COMPETITION
BETWEEN THE IMMUNE SYSTEM AND VIRAL INFECTIONS

Authors

Anka Markovska$^1$, Mikhail Kolev$^2$, Iveta Nikolova$^3$
$^1$Department of Electrical engineering, electronics and automation
Faculty of Engineering
South-West University "Neofit Rilski"
66, Ivan Mihailov Str., Blagoevgrad, 2700, BULGARIA
$^{2,3}$Department of Mathematics
Faculty of Mathematics and Natural Sciences
South-West University "Neofit Rilski"
66, Ivan Mihailov Str., Blagoevgrad, 2700, BULGARIA

Abstract

A mathematical model of adaptive immune response to viral infection is formulated as a system of six ordinary differential equations (ODE). The model describes the interactions between virus, uninfected cells, infected cells, and the adaptive immune response represented by antibodies and two subpopulations of cytotoxic T lymphocytes (CTL): CTL-precursors and CTL-effectors. Theorems of existence, uniqueness and non-negativity of solutions are proven. Primary and secondary immune responses against viral infection are investigated by numerical simulations using Matlab.

History

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

AMS Classification, Key Words

AMS Subject Classification: 65L04, 92C02, 92C06, 92C08
Key Words and Phrases: numerical simulations, ordinary differential equations, nonlinear dynamics, virus, immune system

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Bibliography

1
P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York-London-Sydney (1964).

2
M. Kolev, A. Korpusik, A. Markovska, Adaptive immunity and CTL differentiation - a kinetic modeling approach, Mathematics in Engineering, Science and Aerospace (MESA), 3 (2012), 285-293.

3
L. Shampine, M. Reichelt, The Matlab ODE suite. SIAM J. Sci. Comput., 18 (1997), 1-22.

How to Cite?

DOI: 10.12732/ijpam.v117i2.7 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: 335 - 343


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