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Computational and Mathematical Methods in Medicine
Volume 2015 (2015), Article ID 482091, 12 pages
Research Article

Equilibrium Analysis of a Yellow Fever Dynamical Model with Vaccination

1School of Medicine, University of São Paulo and LIM01 HC-FMUSP, Avenida Doutor Arnaldo 455, Cerqueira César, 01246-903 São Paulo, SP, Brazil
2School of Veterinary Medicine and Zootechnology, University of São Paulo, Avenida Professor Doutor Orlando Marques de Paiva 87, Cidade Universitária, 05508 270 São Paulo, SP, Brazil
3London School of Hygiene and Tropical Medicine, London University, Keppel Street, London WC1E 7HT, UK

Received 6 October 2014; Revised 30 January 2015; Accepted 30 January 2015

Academic Editor: Chung-Min Liao

Copyright © 2015 Silvia Martorano Raimundo 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.


We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies.