Global asymptotic properties of a delay SIR epidemic model with finite incubation times
type: Item
instance of: scholarly article
title: Global asymptotic properties of a delay SIR epidemic model with finite incubation times
zbMATH Open document ID: 0967.34070
DOI: 10.1016/S0362-546X(99)00138-8
author: Yasuhiro Takeuchi
author: Wanbiao Ma
author: E. Beretta
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-11-06T00:00:00Z
review text: Here, the SIR model with distributed delays \[ \begin{aligned} {ds(t)\over dt} & = -\beta s(t) \int^h_0 f(\tau)i(t-\tau) d\tau- \mu_1s(t)+ b,\\ {di(t)\over dt} & =\beta s(t) \int^h_0 f(\tau)i(t- \tau) d\tau- \mu_2i(t)- \lambda i(t),\\ {dr(t)\over dt} & =\lambda i(t)- \mu_3 r(t),\end{aligned} \] is analyzed. By the Lyapunov-Lasalle invariance principle, the authors show that the disease free equilibrium is globally attractive whenever \({b\over\mu_1}\leq s^*= {\mu_2+\lambda\over \beta}\). Sufficient conditions are given to ensure the global asymptotic stability of the endemic equilibrium based on some difference inequality and the construction of Lyapunov functionals.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D23
zbMATH DE Number: 1526167
zbMATH Keywords: epidemic model
zbMATH Keywords: time delay
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: endemic equilibrium
reviewed by: Lansun Chen
MaRDI profile type: Publication
cites work: Q3262986
cites work: Global stability results for a generalized Lotka-Volterra system with distributed delays. Applications to predator-prey and epidemic systems
cites work: Global stability of an SIR epidemic model with time delays
cites work: Convergence results in SIR epidemic models with varying population sizes
cites work: Periodic Solutions of a Periodic Nonlinear Delay Differential Equation
cites work: Stability analysis for a vector disease model
cites work: Theory of functional differential equations. 2nd ed
cites work: Qualitative analyses of communicable disease models
cites work: Delay differential equations: with applications in population dynamics
cites work: Global asymptotic stability for a vector disease model with spatial spread
cites work: Q3680662
cites work: Global asymptotic stability of a periodic solution to an epidemic model
full work available at URL: s0362-546x(99)00138-8
OpenAlex ID: W2049640908
description: scientific article; zbMATH DE number 1526167