Next Article in Journal
Kinematics in the Information Age
Previous Article in Journal
L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New?
Previous Article in Special Issue
Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters
Article Menu

Export Article

Open AccessArticle
Mathematics 2018, 6(9), 147; https://doi.org/10.3390/math6090147

Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
Received: 21 July 2018 / Revised: 22 August 2018 / Accepted: 22 August 2018 / Published: 23 August 2018
(This article belongs to the Special Issue Applied Analysis of Ordinary Differential Equations)
Full-Text   |   PDF [431 KB, uploaded 23 August 2018]   |  

Abstract

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings. View Full-Text
Keywords: SIR epidemic model; age structure; endemic equilibrium; stability; basic reproduction number SIR epidemic model; age structure; endemic equilibrium; stability; basic reproduction number
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Kuniya, T. Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs. Mathematics 2018, 6, 147.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top