Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence

Pei Yu; Wenjing Zhang; Lindi M. Wahl

doi:10.1016/j.cnsns.2015.12.022

Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence

Pei Yu, Wenjing Zhang, Lindi M. Wahl

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	163-192
Number of pages	30
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	37
DOIs	https://doi.org/10.1016/j.cnsns.2015.12.022
State	Published - Aug 1 2016

Keywords

Bogdanov-Takens (BT) bifurcation
Dynamical system
HIV viral blips
Homoclinic orbit
Hopf and generalized Hopf bifurcations
Recurrent autoimmune disease
Recurrent infection
Stability and bifurcation

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10.1016/j.cnsns.2015.12.022

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title = "Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence",

abstract = "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.",

keywords = "Bogdanov-Takens (BT) bifurcation, Dynamical system, HIV viral blips, Homoclinic orbit, Hopf and generalized Hopf bifurcations, Recurrent autoimmune disease, Recurrent infection, Stability and bifurcation",

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AU - Yu, Pei

AU - Zhang, Wenjing

AU - Wahl, Lindi M.

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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

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DO - 10.1016/j.cnsns.2015.12.022

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AN - SCOPUS:84959258253

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SP - 163

EP - 192

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

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