Stochastic regime switching SIS epidemic model with vaccination driven by L\xe9vy noise

Yingjia Guo

doi:10.1186/s13662-017-1424-7

Abstract

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Highlights

1 Introduction It is well known that epidemic diseases always bring great harm to the stability of the social and threat individual health, the rapid development of society and frequent contacts among people can accelerate the spread of epidemic disease
In Sections and, we investigate the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by a Lévy noise
If Di(k, u) = (i =, ), Theorem . shows that the solution of the stochastic regime switching SIS model with vaccination will fluctuate around a certain level relevant to Ek∗ and σi(k) (i =, )

Summary

Introduction

It is well known that epidemic diseases (tuberculosis, SARS, AIDS, etc.) always bring great harm to the stability of the social and threat individual health, the rapid development of society and frequent contacts among people can accelerate the spread of epidemic disease. Guo Advances in Difference Equations (2017) 2017:375 between compartments S and I, μ is the natural death rate per capita, p represents the proportional coefficient of vaccinated for the susceptible, γ is the recovery rate, ε is the rate of losing immunity for vaccinated individuals, and α represents the disease-caused death rate of infectious individuals These parameter values are all nonnegative, and μ, A >. Bao et al suggested that the non-Gaussian Lévy noise should be suitable for describing these phenomena [ – ] They considered stochastic Lotka-Volterra population systems with jumps [ ] for the first time, and some important results that reveal that jump processes can bring their effect on the properties of the systems have been reported [ – ]. ). In Sections and , we investigate the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by a Lévy noise

Preliminaries

Conclusions