Global phase portraits of a SIS model
Oliveira, Regilene (Universidade de Sâo Paulo(Brazil). Departamento de Matemática)
Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	In the qualitative theory of ordinary differential equations, we can find many papers whose objective is the classification of all the possible topological phase portraits of a given family of differential system. Most of the studies rely on systems with real parameters and the study consists of outlining their phase portraits by finding out some conditions on the parameters. Here, we studied a susceptible-infected-susceptible (SIS) model described by the differential system x˙ = −bxy − mx + cy + mk, y˙ = bxy − (m + c)y, where b, c, k, m are real parameters with b 6= 0, m 6= 0 [3]. Such system describes an infectious disease from which infected people recover with immunity against reinfection. The integrability of such system has already been studied by Nucci and Leach [8] and Llibre and Valls [6]. We found out two different topological classes of phase portraits.
Note:	Agraïments: Both authors are supported by the joint project CAPES/DGU grant 222/2010. The second author has been supported by a Ph.D. CAPES grant.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	SIS epidemic model ; Global phase portrait ; Endemic and disease-free steady states
Published in:	Applied Mathematics and Computation, Vol. 219 Núm. 9 (2013) , p. 4924-4930, ISSN 0096-3003

DOI: 10.1016/j.amc.2012.10.090

Postprint 12 p, 379.5 KB

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