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Bifurcation and chaos in an epidemic model with nonlinear incidence rates. (English) Zbl 1187.92073
Summary: This paper investigates a discrete-time epidemic model by qualitative analysis and numerical simulations. It is verified that there are phenomena of transcritical bifurcation, flip bifurcation, Hopf bifurcation types and chaos. Also the largest Lyapunov exponents are numerically computed to confirm further the complexity of these dynamic behaviors. The obtained results show that discrete epidemic model can have rich dynamical behavior.
MSC:
92D30Epidemiology
34C23Bifurcation (ODE)
37N25Dynamical systems in biology
65C20Models (numerical methods)
34C60Qualitative investigation and simulation of models (ODE)
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