Geodesic
Global stability of a vaccination model with immigration
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study an SVIR model of disease transmission with immigration into all four classes. Vaccinated individuals may only receive partial immunity to the disease, giving a leaky vaccine. The incidence function permits a nonlinear response to the number of infectives, so that mass action and saturating incidence are included as special cases. Because of the immigration of infected individuals, there is no disease-free equilibrium and hence no basic reproduction number. We use the Brouwer Fixed Point Theorem to show that an endemic equilibrium exists and the Poincare-Hopf Theorem to show that it is unique. We show the equilibrium is globally asymptotically stable by using a Lyapunov function.
Classification : 34K20, 92D30
Keywords: global stability, Lyapunov function, epidemiology, immigration 
@article{EJDE_2015__2015__a54,
     author = {Henshaw, Sarah and McCluskey, C.Connell},
     title = {Global stability of a vaccination model with immigration},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a54/}
}
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Henshaw, Sarah; McCluskey, C.Connell. Global stability of a vaccination model with immigration. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a54/