title: Equilibrium analysis of a yellow Fever dynamical model with vaccination.
abstract: 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.
authors.affiliation: School of Medicine, University of São Paulo and LIM01 HC-FMUSP, Avenida Doutor Arnaldo 455, Cerqueira César, 01246-903 São Paulo, SP, Brazil.
authors.forename: Silvia
authors.initials: S
authors.lastname: Martorano Raimundo
authors.affiliation: School 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.
authors.forename: Marcos
authors.identifier: 0000-0003-4752-6774
authors.initials: M
authors.lastname: Amaku
authors.affiliation: School of Medicine, University of São Paulo and LIM01 HC-FMUSP, Avenida Doutor Arnaldo 455, Cerqueira César, 01246-903 São Paulo, SP, Brazil ; London School of Hygiene and Tropical Medicine, London University, Keppel Street, London WC1E 7HT, UK.
authors.forename: Eduardo
authors.identifier: 0000-0002-7200-2916
authors.initials: E
authors.lastname: Massad
mesh_terms: D000465:Algorithms; D000818:Animals; D003140:Communicable Disease Control; D003198:Computer Simulation; D009033:Culicidae / Q000821:virology; D018177:Flavivirus Infections; D006801:Humans; D055552:Infectious Disease Medicine / Q000379:methods; D007303:Insect Vectors / Q000821:virology; D008962:Models, Theoretical; D015995:Prevalence; D014611:Vaccination / Q000379:methods*; D015004:Yellow Fever / Q000821:virology*
references.citation: Comput Math Methods Med. 2013;2013:659038
references.pmid: 24454539
references.citation: Annu Rev Entomol. 2007;52:209-29
references.pmid: 16913829
references.citation: Bull Math Biol. 2014 Mar;76(3):697-717
references.pmid: 24619807
references.citation: Lancet Infect Dis. 2001 Aug;1(1):11-20
references.pmid: 11871403
references.citation: J Invertebr Pathol. 2003 Sep;84(1):24-9
references.pmid: 13678709
references.citation: Rev Saude Publica. 1993 Aug;27(4):227-36
references.pmid: 7911592
references.citation: Math Biosci. 1994 Oct;123(2):227-47
references.pmid: 7827421
references.citation: Am J Trop Med Hyg. 2004 Oct;71(4):506-13
references.pmid: 15516650
references.citation: Vaccine. 2005 Jun 10;23(30):3908-14
references.pmid: 15917112
references.citation: Bull Math Biol. 2006 Nov;68(8):2263-82
references.pmid: 16952019
references.citation: Epidemiol Infect. 2008 Mar;136(3):309-19
references.pmid: 17540051
references.citation: Bull Math Biol. 2008 Jul;70(5):1272-96
references.pmid: 18293044
references.citation: Curr Probl Pediatr Adolesc Health Care. 2009 Apr;39(4):97-140
references.pmid: 19327647
references.citation: Malar J. 2009;8:296
references.pmid: 20015392
references.citation: Phys Life Rev. 2011 Jun;8(2):169-99
references.pmid: 21257353
references.citation: Rev Soc Bras Med Trop. 2011 May-Jun;44(3):290-6
references.pmid: 21739073
references.citation: Biosystems. 2011 Nov;106(2-3):111-20
references.pmid: 21839800
references.citation: Rev Saude Publica. 2013 Oct;47(5):881-9
references.pmid: 24626492