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The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2015年01期
Page:
1-
Research Field:
数学
Publishing date:

Info

Title:
The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations
Author(s):
Jiang Guirong; Lin Jiao; Liu Suyu
School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China
Keywords:
SIRS model; standard incidence; transcritical bifurcation; flip bifurcation
PACS:
O175.1
DOI:
-
Abstract:
Birth pulse,vertical transmission,and pulse treatment are considered in an SIRS model. The dynamical behavior of an SIRS epidemic model with standard incidence is discussed by means of both theoretical and numerical ways. Firstly,by using Floquet theory,the existence and stability of the trivial solution,infection-free periodic solution,and epidemic periodic solution are proved. Secondly,the Poincare map,center manifold theorem,and bifurcation theorem are used to discuss transcritical bifurcation and flip bifurcation.The numerical results,which are illustrated with an example,are in good agreement with the theoretical analysis. Finally,biological explanations and main conclusions are given.

References:

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Last Update: 2015-03-30