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Abstract and Applied Analysis
Volume 2015, Article ID 341854, 8 pages
http://dx.doi.org/10.1155/2015/341854
Research Article

Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age

1Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, Avenida Universidad, 3000 Circuito Exterior, S/N, 04510 Delegación Coyoacán, DF, Mexico
2Centro de Ciencias de la Complejidad (C3), Torre de Ingeniería, UNAM, Ciudad Universitaria, Avenida Universidad, 3000 Circuito Exterior, S/N, 04510 Delegación Coyoacán, DF, Mexico
3Unidad de Medicina Experimental, Hospital General de México, Dr Balmis No. 148., Colonia Doctores, 06726 México, DF, Mexico

Received 22 November 2014; Accepted 12 January 2015

Academic Editor: Yanni Xiao

Copyright © 2015 Raúl Peralta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states.