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Disease transmission models with density-dependent demographics. (English) Zbl 0774.92018
SIRS and SIS type models for the spread of an infectious disease are considered in which the total population size is logistic (unlike most models in which total population size is assumed constant). Using a combination of local, global, and numerical analyses the authors study equilibria and stability. Generally the disease results in extinction or in an equilibrium that is below the natural carrying capacity.

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