|Table of Contents|

The Stability Analysis of an SEIRS Model(PDF)

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

Issue:
2013年03期
Page:
21-30
Research Field:
数学
Publishing date:

Info

Title:
The Stability Analysis of an SEIRS Model
Author(s):
Fang Lingling1; Qi Longxing2
(1.Basic Course Teaching Department,JiangXi University of Technology,Nanchang 330098,China) (2.School of Mathematical Sciences,Anhui University,Hefei 230601,China)
Keywords:
SEIRS model; nonlinear incidence; stability; vertical transmission; time delay
PACS:
O175.25
DOI:
-
Abstract:
In this paper,nonlinear incidence with a more general form is considered in an SEIRS epidemic model.The model without time delay in the removed class is compared with the model with time delay in the removed class.The result shows that the dynamic behaviors of the model with time delay are different from those of the model without delay.For the model without time delay,the disease free equilibrium(DFE)is globally asymptotically stable when the basic reproduction number is smaller than one.When the basic reproduction number is bigger than one,regardless of the time delay length there exists a unique endemic equilibrium which is locally asymptotically stable under a condition.As for the model with time delay,the stability of the DFE depends on the time delay besides the basic reproduction number.Furthermore,the stability of the unique endemic equilibrium can be obtained under some conditions depending on the time delay.In addition,by numerical simulations,periodic solutions can be found from the endemic equilibrium when the time delay is in some regions.

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Last Update: 2013-09-30