Global dynamics of a virus model with invariant algebraic surfaces
Dias, Fabio Scalco (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)

Date:	2019
Abstract:	In this paper by using the Poincaré compactification in R3 we make a global analysis for the virus system x˙=λ-dx-βxz,y˙=-ay+βxz z˙=ky-μz with (x, y, z) ∈ R3, β> 0, λ, a, d, k and μ are nonnegative parameters due to their biological meaning. We give the complete description of its dynamics on the sphere at infinity. For two sets of the parameter values the system has invariant algebraic surfaces. For these two sets we provide the global phase portraits of the virus system in the Poincaré ball (i. e. in the compactification of R3 with the sphere S2 of the infinity).
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Invariant algebraic surfaces ; Poincaré compactification ; Phase portrait ; Dynamics at infinity ; Virus model
Published in:	Rendiconti del Circolo Matematico di Palermo, vol. 69 (May 2019) p.535-546, ISSN 1973-4409

DOI: 10.1007/s12215-019-00417-0

Post-print 14 p, 324.3 KB

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