Asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

Author:

Xu Yuncheng12,Liu Sanyang1,Sun Xiaojun3,Hu Hua2,Wang Yu4

Affiliation:

1. School of Mathematics and Statistics, Xidian University, Xi’an 710071, P. R. China

2. School of Mathematics and Statistics, Ning Xia University, Ningxia 750021, P. R. China

3. School of Mathematics and Information Science, Bao Ji University of Arts and Sciences, Baoji 721013, P. R. China

4. College of Mathematics Science and Center, for Applied Mathematical Science, Inner Mongolia Normal University, Hohhot 010022, P. R. China

Abstract

To investigate the effect of information transmission, Lévy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic, a stochastic SIQR epidemic model with non-monotone incidence rate and Lévy jumps on scale-free networks is constructed. At first, the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions. Then the stochastic model is made in accordance with the ecological significance, the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested. Next, by constructing suitable stochastic Lyapunov functions and applying Itô formula with jump, the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked. At last, the correctness of the analytical results is verified by numerical simulations.

Funder

Natural Science Foundation of Ningxia

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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