JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (5): 10-17.doi: 10.6040/j.issn.1671-9352.0.2016.531

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Dynamics of a stochastic SIS epidemic model with different incidences and double epidemic hypothesis

ZHANG Dao-xiang1,2, HU Wei1, TAO Long1, ZHOU Wen1   

  1. 1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China;
    2. Department of Mathematics and Statistics, University of Helsinki, Helsinki 00014, Finland
  • Received:2016-11-18 Online:2017-05-20 Published:2017-05-15

Abstract: We propose a new mathematical model with two different incidence rates and double epidemic hypothesis. By the Lyapunov function and Itôs formula, we explore and obtain the threshold of a stochastic SIS system for the extinction and thepermanence in mean of two epidemic diseases. The results show that not only a large stochastic disturbance but also a small stochastic disturbance can cause infectious diseases to go to extinction.

Key words: stochastic epidemic model, extinction, threshold, permanence

CLC Number: 

  • Q332
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