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Some infectious disease models with population dynamics and general contact rates. (English) Zbl 0722.92014
Two models for infectious diseases are considered. One allowing recovery without immunity and the other allowing recovery with full immunity. These models, as usual, are represented by non-linear equations. It is shown that there is a single asymptotically stable equilibrium for diseases with recovery either with no immunity or with full immunity. The equilibrium is the disease-free equilibrium if the contact number is less than one and an endemic equilibrium if the contact number is greater than one.

92D30 Epidemiology
34K20 Stability theory of functional-differential equations