TY - JOUR
T1 - Global dynamics of a virus model with invariant algebraic surfaces
AU - Dias, Fabio Scalco
AU - Llibre, Jaume
AU - Valls, Claudia
N1 - Publisher Copyright:
© 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - 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+βxzz˙=ky-μzwith (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).
AB - 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+βxzz˙=ky-μzwith (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).
KW - Dynamics at infinity
KW - Invariant algebraic surfaces
KW - Phase portrait
KW - Poincaré compactification
KW - Virus model
UR - https://www.scopus.com/pages/publications/85065251080
U2 - 10.1007/s12215-019-00417-0
DO - 10.1007/s12215-019-00417-0
M3 - Article
AN - SCOPUS:85065251080
SN - 0009-725X
VL - 69
SP - 535
EP - 546
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 2
ER -