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Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious diseases with periodic contact rates and disease-dependent demographic factors in the population. (English) Zbl 1018.92030

Summary: Within the framework of SEIR-like epidemic models, we studied the conditions for stable eradication of some families of vertically and horizontally transmitted infectious diseases in the case of periodically varying contact rates. By means of Floquet’s theory, we found a condition for the eradication solution to be locally asymptotically stable. We then demonstrated that the same condition guarantees also that this vaccine-induced disease-free solution is globally asymptotically stable.
A model with interacting populations is also considered. In the final part of this work, we extended the model by taking into account the variation of population size, the impact of disease-related deaths and reduction of fertility.

MSC:

92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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