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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 6


Stability and Hopf Bifurcation in a Delayed SIS Epidemic Model with Double Epidemic Hypothesis

Jiangang Zhang / Yandong Chu / Wenju Du / Yingxiang Chang / Xinlei An
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/ijnsns-2016-0122


The stability and Hopf bifurcation of a delayed SIS epidemic model with double epidemic hypothesis are investigated in this paper. We first study the stability of the unique positive equilibrium of the model in four cases, and we obtain the stability conditions through analyzing the distribution of characteristic roots of the corresponding linearized system. Moreover, we choosing the delay as bifurcation parameter and the existence of Hopf bifurcation is investigated in detail. We can derive explicit formulas for determining the direction of the Hopf bifurcation and the stability of bifurcation periodic solution by center manifold theorem and normal form theory. Finally, we perform the numerical simulations for justifying the theoretical results.

Keywords: delayed SIS epidemic model; double epidemic hypothesis; stability; Hopf bifurcation

PACS: 2010; 110.51


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About the article

Received: 2016-08-25

Accepted: 2018-01-09

Published Online: 2018-07-20

Published in Print: 2018-09-25

This work was supported by the National Natural Science Foundation; [11161027]; [61364001]; Science and Technology Program of Gansu Province; [144GKCA018].

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 6, Pages 561–571, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0122.

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