General models of host-parasite systems. Global analysis.
Résumé
This paper considers the global behavior of general models of host-parasite sysytems. The authors discuss the model with k classes of age, with and without the gametocytes production in section 2. The model of Anderson-May-Gupta with two distinct genotype and production of gameetypes is also investigated in section 3. By using a Lyapunov function and Lasalle's invariance principle, they 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. A competitive exclusion principle holds. This means that a unique equilibrium, corresponding to the extinction of one strain and the survival of the other strain, is globally asymptotically stable on the positive orthant if the value of the basic reproduction ratio is less than one.