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General models of host-parasite systems. Global analysis

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  • We obtain global stability results for within-host models with $k$ age-class of parasitized cells and two strains of parasites. The stability is determined by the value of the basic reproduction ratio $\mathcal R_0$. A competitive exclusion principle holds. This means that if $\mathcal R_0 >1$ generically an unique equilibrium, corresponding to the extinction of one strain and the survival of the other strain, is globally asymptotically stable on the positive orthant.
    Mathematics Subject Classification: Primary: 34D23, 34A34; Secondary: 92D30.

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