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Dynamical behavior of epidemiological models with nonlinear incidence rates. (English) Zbl 0621.92014

Epidemiological models with nonlinear incidence rates λI p S q show a much wider range of dynamical behaviors than do those with bilinear incidence rates λ IS. These behaviors are determined mainly by p and λ, and secondarily by q.

For such models, there may exist multiple attractive basins in phase space; thus whether or not the disease will eventually die out may depend not only upon the parameters, but also upon the initial conditions. In some cases, periodic solutions may appear by Hopf bifurcation at critical parameter values.


MSC:
92D25Population dynamics (general)
34D99Stability theory of ODE
34C25Periodic solutions of ODE
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