𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global behaviour of an SIR epidemic model with time delay

✍ Scribed by Jean M. Tchuenche; Alexander Nwagwo; Richard Levins

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
166 KB
Volume
30
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study the stability of a delay susceptible–infective–recovered epidemic model with time delay. The model is formulated under the assumption that all individuals are susceptible, and we analyse the global stability via two methods—by Lyapunov functionals, and—in terms of the variance of the variables. The main theorem shows that the endemic equilibrium is stable. If the basic reproduction number ℛ~0~ is less than unity, by LaSalle invariance principle, the disease‐free equilibrium E~s~ is globally stable and the disease always dies out. By applying the integral averaging theory, we also investigate the stability in variance of the model. Copyright © 2006 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Erratum: ‘Global behaviour of an SIR epi
Erratum: ‘Global behaviour of an SIR epidemic model with time delay’
✍ Jean M. Tchuenche; Alexander Nwagwo; Richard Levins 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 56 KB

In [1], there was a typographical error in the entries of the off-diagonal elements of the matrix A(t), starting on the line before Equation ( 15). The purpose of this current note is to correct this mistake and propose a direction for future work. Choose W 1 , W 2 > 0 such that W 2 = W 1 e -h I \*

Local stability of an SIR epidemic model
Local stability of an SIR epidemic model and effect of time delay
✍ Jean M. Tchuenche; Alexander Nwagwo 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 173 KB

## Abstract We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stab

Global Stability of Discrete Population
Global Stability of Discrete Population Models with Time Delays and Fluctuating Environment
✍ Wang Wendi; G. Mulone; F. Salemi; V. Salone 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 139 KB

The global stability of a discrete population model of Volterra type is studied. The model incorporates time delays and allows for a fluctuating environment. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure a p