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Geng Y, Xu J. Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation. INT J BIOMATH 2020. [DOI: 10.1142/s1793524520500333] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells. The global asymptotic stabilities of the equilibria are studied by constructing Lyapunov functionals. Moreover, we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation parameters. The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation. Finally, numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.
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Affiliation(s)
- Yan Geng
- School of Science, Xi’an Polytechnic University, Xi’an 710048, Shaanxi, P. R. China
| | - Jinhu Xu
- School of Sciences, Xi’an University of Technology, Xi’an 710049, Shaanxi, P. R. China
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Song L, Ma C, Li Q, Fan A, Wang K. Global dynamics of a viral infection model with full logistic terms and antivirus treatments. INT J BIOMATH 2016. [DOI: 10.1142/s1793524517500127] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus (HCV) dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus (HBV) or human immunodeficiency virus (HIV) infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number [Formula: see text] is a sharp threshold para-meter for the outcomes of viral infections. If [Formula: see text], the virus-free equilibrium is globally asymptotically stable. If [Formula: see text], the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another sufficient condition is obtained by Li–Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.
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Affiliation(s)
- Lijuan Song
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
| | - Cui Ma
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
| | - Qiang Li
- Center for Hypertension and Metabolic Diseases, Department of Hypertension and Endocrinology, Daping Hospital, Third Military Medical University, Chongqing 400038, P. R. China
- Chongqing Institute of Hypertension, Chongqing 400042, P. R. China
| | - Aijun Fan
- Chongqing Academy of Science and Technology, Chongqing 401123, P. R. China
| | - Kaifa Wang
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
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