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

Advances in Difference Equations

Anqi Miao¹  Xinyang Wang¹  Tongqian Zhang¹  BG Sampath Aruna Pradeep²  Wei Wang³ 

[1] College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, P.R. China;School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, P.R. China;State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, P.R. China

关键词: stochastic SIS epidemic model;    double epidemic hypothesis;    Beddington-DeAngelis incidence rate;    extinction;    permanence;    60H10;    65C30;    91B70;   

DOI  :  10.1186/s13662-017-1289-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY