Stability and Bifurcations in an Epidemic Model with Varying Immunity Period

Blyuss, Konstantin B and Kyrychko, Yuliya N (2010) Stability and Bifurcations in an Epidemic Model with Varying Immunity Period. Bulletin of Mathematical Biology, 72 (2). pp. 490-505. ISSN 0092-8240

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Abstract

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different values of system parameters and different integral kernels.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Konstantin Blyuss
Date Deposited: 06 Feb 2012 18:12
Last Modified: 08 Jun 2012 15:22
URI: http://sro.sussex.ac.uk/id/eprint/15244
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