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Demography and epidemics. (English) Zbl 0751.92012
A demographic SIR epidemic model with vertical transmission of homogeneous type is studied. The hypothesis of homogeneity is assumed to model the interaction of epidemic and demographic features. General properties of homogeneous evolution equations and a generalized version of the Dulac criterion adapted to the homogeneous problem are applied to get insight into the simplest situation of constant coefficients. The nonexistence of periodic solutions is shown and a threshold condition is obtained concerning the stability of exponential solutions of the model.

MSC:
92D30 Epidemiology
92D25 Population dynamics (general)
34C99 Qualitative theory for ordinary differential equations
37-XX Dynamical systems and ergodic theory
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