Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis

In this paper, a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis is proposed and analysed. We explain the effects of stochastic disturbance on disease transmission. To this end, firstly, we investigated the dynamic properties of the system neglecting stocha...

Full description

Saved in:
Bibliographic Details
Published in:Advances in difference equations 2017-08, Vol.2017 (1), p.1-27, Article 226
Main Authors: Miao, Anqi, Wang, Xinyang, Zhang, Tongqian, Wang, Wei, Sampath Aruna Pradeep, BG
Format: Article
Language:English
Subjects:
Analysis
Beddington-DeAngelis incidence rate
Computer simulation
Difference and Functional Equations
double epidemic hypothesis
Economic models
Epidemics
Extinction
Functional Analysis
Hypotheses
Incidence
Infectious diseases
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
permanence
Probability theory
Randomness
stochastic SIS epidemic model
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis is proposed and analysed. We explain the effects of stochastic disturbance on disease transmission. To this end, firstly, we investigated the dynamic properties of the system neglecting stochastic disturbance and obtained the threshold and the conditions for the extinction and the permanence of two kinds of epidemic diseases by considering the stability of the equilibria of the deterministic system. Secondly, we paid prime attention on the threshold dynamics of the stochastic system and established the conditions for the extinction and the permanence of two kinds of epidemic diseases. We found that there exists a significant difference between the threshold of the deterministic system and that of the stochastic system. Moreover, it has been established that the persistent of infectious disease analysed by use of deterministic system becomes extinct under the same conditions due to the stochastic disturbance. This implies that a stochastic disturbance has significant impact on the spread of infectious diseases and the larger stochastic disturbance leads to control the epidemic diseases. In order to illustrate the dynamic difference between the deterministic system and the stochastic system, there have been given a series of numerical simulations by using different noise disturbance coefficients.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-017-1289-9