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Qualitative analysis and travelling wave solutions for the SI model with vertical transmission

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  • In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. For a bounded spatial domain we show global stability of the endemic state when it is feasible. Then we look at the existence of travelling wave solutions connecting the endemic and the disease free states.
    Mathematics Subject Classification: Primary: 35A18, 35B35, 35B40, 35K57; Secondary: 92D30.

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