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Title: Stability analysis of the Euler discretization for SIR epidemic model

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.
Authors:
 [1]
  1. Department of Mathematics, Faculty of Sciences, Brawijaya University, Jl. Veteran Malang 65145 (Indonesia)
Publication Date:
OSTI Identifier:
22311272
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1602; Journal Issue: 1; Conference: 3. international conference on mathematical sciences, Kuala Lumpur (Malaysia), 17-19 Dec 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; COMPUTERIZED SIMULATION; DISEASES; EQUILIBRIUM; MATHEMATICAL MODELS; NUMERICAL SOLUTION; STABILITY