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Dynamical behavior of epidemiological models with nonlinear incidence rates. (English) Zbl 0621.92014
Epidemiological models with nonlinear incidence rates \(\lambda I^ pS^ q\) show a much wider range of dynamical behaviors than do those with bilinear incidence rates \(\lambda\) IS. These behaviors are determined mainly by p and \(\lambda\), 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:
92D25 Population dynamics (general)
34D99 Stability theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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