Analysis of a Delayed SIR Model with Nonlinear Incidence Rate

Jin-Zhu Zhang, Zhen Jin, Quan-Xing Liu and Zhi-Yu Zhang

Discrete Dynamics in Nature and Society, 2008, vol. 2008, 1-16

Abstract:

An SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. The threshold value determining whether the disease dies out is found. The results obtained show that the global dynamics are completely determined by the values of the threshold value and time delay (i.e., incubation time length). If is less than one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, while if it exceeds one there will be an endemic. By using the time delay as a bifurcation parameter, the local stability for the endemic equilibrium is investigated, and the conditions with respect to the system to be absolutely stable and conditionally stable are derived. Numerical results demonstrate that the system with time delay exhibits rich complex dynamics, such as quasiperiodic and chaotic patterns.

Date: 2008
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2008/636153.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2008/636153.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:636153

DOI: 10.1155/2008/636153

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().