A GENERAL UNIQUENESS RESULT OF AN ENDEMIC STATE FOR AN EPIDEMIC MODEL WITH EXTERNAL FORCE OF INFECTION

- Journal title : Communications of the Korean Mathematical Society
- Volume 22, Issue 4, 2007, pp.597-608
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2007.22.4.597

Title & Authors

A GENERAL UNIQUENESS RESULT OF AN ENDEMIC STATE FOR AN EPIDEMIC MODEL WITH EXTERNAL FORCE OF INFECTION

Cha, Young-Joon;

Cha, Young-Joon;

Abstract

We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.

Keywords

endemic;S-I-R;uniqueness;inter-cohort;external force;

Language

English

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