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Models for the spread of universally fatal diseases. (English) Zbl 0718.92021
Summary: In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibria may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.

MSC:
92D30 Epidemiology
34D99 Stability theory for ordinary differential equations
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