On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination
De la Sen, Manuel (Universidad del País Vasco. Departamento de Electricidad y Electrónica)
Agarwal, Ravi P. (King Fahd University of Petroleum and Minerals. Mathematics and Statistics Department)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)
Alonso-Quesada, Santiago (Universidad del País Vasco. Departamento de Electricidad y Electrónica)

Date:	2011
Abstract:	This paper discusses the disease-free and endemic equilibrium points of a SVEIRS propagation disease model which potentially involves a regular constant vaccination. The positivity of such a model is also discussed as well as the boundedness of the total and partial populations. The model takes also into consideration the natural population growing and the mortality associated to the disease as well as the lost of immunity of newborns. It is assumed that there are two finite delays affecting the susceptible, recovered, exposed, and infected population dynamics. Some extensions are given for the case when impulsive nonconstant vaccination is incorporated at, in general, an aperiodic sequence of time instants. Such an impulsive vaccination consists of a culling or a partial removal action on the susceptible population which is transferred to the vaccinated one. The oscillatory behavior under impulsive vaccination, performed in general, at nonperiodic time intervals, is also discussed.
Grants:	Ministerio de Educación y Ciencia DPI2009-07197
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Equilibrium point ; Epidemic model ; Endemic equilibrium ; Susceptible population ; Infected population
Published in:	Advances in difference equations, Vol. 2011 (2011) , art. 748608, ISSN 1687-1847

DOI: 10.1155/2011/748608

32 p, 974.4 KB

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