IJPAM: Volume 106, No. 3 (2016)

STOCHASTIC STABILITY OF VECTOR SDE WITH
APPLICATIONS TO A STOCHASTIC EPIDEMIC MODEL

Anatoliy Swishchuk$^1$, Mariya Svishchuk$^2$, Nikolaos Limnios$^3$
$^1$University of Calgary
2500 University Drive NW
Calgary, AB, T2N 1N4, CANADA
$^2$Mount Royal University
4825 Mt Royal Gate SW
Calgary, AB T3E 6K6, CANADA
$^3$University Technology of Compiegne
BP 20529, 60205
Compiegne Cedex, FRANCE


Abstract. In this paper we consider stochastic stability, namely, asymptotic stability in mean, asymptotic mean-square stability, asymptotic stability a.s., exponential $p$-stability and stability with stochastic Lyapunov fucntion for vector stochastic differential equations. We apply these results to the stochastic epidemic models induced by bacteriophages in the marine bacteria populations. The novelty of the paper consists of new stability results for vector SDE and their applications to a new stochastic epidemic model.

Received: December 4, 2015

AMS Subject Classification: 34F05, 34E10, 60K15, 34D20, 34D05, 92D30

Key Words and Phrases: vector SDE, stochastic stabilities, Lyapunov function, stochastic epidemic model, marine bacteria populations

Download paper from here.




DOI: 10.12732/ijpam.v106i3.9 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: 2016
Volume: 106
Issue: 3
Pages: 801 - 839


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).