Stability analysis of the Euler discretization for SIR epidemic model
- Department of Mathematics, Faculty of Sciences, Brawijaya University, Jl. Veteran Malang 65145 (Indonesia)
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.
- OSTI ID:
- 22311272
- Journal Information:
- AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1602; ISSN APCPCS; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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