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An epidemiological model with a delay and a nonlinear incidence rate. (English) Zbl 0714.92021

Summary: An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state.

MSC:

92D30 Epidemiology
45J05 Integro-ordinary differential equations
45M10 Stability theory for integral equations
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References:

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