TY - JOUR
T1 - The complete classification for global dynamics of a model for the persistence of HTLV-I infection
AU - Vargas-De-León, Cruz
PY - 2014/6/15
Y1 - 2014/6/15
N2 - Li and Lim (2011) [8] proposed a three-dimensional system of ordinary differential equations modeling the role of Tax expression in the persistence of Human T-lymphotropic virus Type I and presented a mathematical analysis and its immunovirological explanation. The previous paper shows that three-dimensional system is a cooperative system if a sharp condition is satisfied. By means of the theory of cooperative dynamical systems, they studied the global dynamics. If the sharp condition is not satisfied, they leave it an open problem. The present paper is to provide a complete classification of global dynamics for this ODE model. In particular, our global analysis establishes that the dynamics of the HTLV-I infection are completely determined by a basic reproductive number, which completely solves the open problem above.
AB - Li and Lim (2011) [8] proposed a three-dimensional system of ordinary differential equations modeling the role of Tax expression in the persistence of Human T-lymphotropic virus Type I and presented a mathematical analysis and its immunovirological explanation. The previous paper shows that three-dimensional system is a cooperative system if a sharp condition is satisfied. By means of the theory of cooperative dynamical systems, they studied the global dynamics. If the sharp condition is not satisfied, they leave it an open problem. The present paper is to provide a complete classification of global dynamics for this ODE model. In particular, our global analysis establishes that the dynamics of the HTLV-I infection are completely determined by a basic reproductive number, which completely solves the open problem above.
KW - HTLV-I infection
KW - Logistic growth term
KW - Mitotic transmission
KW - Role of Tax expression
KW - Volterra-type Lyapunov function
UR - http://www.scopus.com/inward/record.url?scp=84899079385&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.03.138
DO - 10.1016/j.amc.2014.03.138
M3 - Artículo
SN - 0096-3003
VL - 237
SP - 489
EP - 493
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -