Stability and Hopf Bifurcation in a Delayed SIS Epidemic Model with Double Epidemic Hypothesis
| Autor: | Yan-Dong Chu, Wenju Du, Ying-Xiang Chang, Xin-lei An, Jian-Gang Zhang |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Hopf bifurcation
Applied Mathematics Computational Mechanics General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences Stability (probability) 010305 fluids & plasmas symbols.namesake Mechanics of Materials Modeling and Simulation 0103 physical sciences symbols Applied mathematics Epidemic model 010301 acoustics Engineering (miscellaneous) Mathematics |
| Zdroj: | International Journal of Nonlinear Sciences and Numerical Simulation. 19:561-571 |
| ISSN: | 2191-0294 1565-1339 |
| DOI: | 10.1515/ijnsns-2016-0122 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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