TY - JOUR
T1 - Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence
AU - Yu, Pei
AU - Zhang, Wenjing
AU - Wahl, Lindi M.
N1 - Funding Information:
Insightful comments from the anonymous referees are greatly appreciated. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC no. R2686A02 and no. 238389-RGPIN).
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - In this paper, a previously developed 2-dimensional disease model is studied, which can be used for both epidemiologic modeling and in-host disease modeling. The main attention of this paper is focused on various dynamical behaviors of the system, including Hopf and generalized Hopf bifurcations which yield bistability and tristability, Bogdanov-Takens bifurcation, and homoclinic bifurcation. It is shown that the Bogdanov-Takens bifurcation and homoclinic bifurcation provide a new mechanism for generating disease recurrence, that is, cycles of remission and relapse such as the viral blips observed in HIV infection.
AB - In this paper, a previously developed 2-dimensional disease model is studied, which can be used for both epidemiologic modeling and in-host disease modeling. The main attention of this paper is focused on various dynamical behaviors of the system, including Hopf and generalized Hopf bifurcations which yield bistability and tristability, Bogdanov-Takens bifurcation, and homoclinic bifurcation. It is shown that the Bogdanov-Takens bifurcation and homoclinic bifurcation provide a new mechanism for generating disease recurrence, that is, cycles of remission and relapse such as the viral blips observed in HIV infection.
KW - Bogdanov-Takens (BT) bifurcation
KW - Dynamical system
KW - HIV viral blips
KW - Homoclinic orbit
KW - Hopf and generalized Hopf bifurcations
KW - Recurrent autoimmune disease
KW - Recurrent infection
KW - Stability and bifurcation
UR - http://www.scopus.com/inward/record.url?scp=84959258253&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2015.12.022
DO - 10.1016/j.cnsns.2015.12.022
M3 - Article
AN - SCOPUS:84959258253
VL - 37
SP - 163
EP - 192
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -