34C05, 92D25.

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

Global properties of a delayed SIR epidemic model with multiple parallel infectious stages

1. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street Harbin, 150080 and College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000
2. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080

## Abstract    Related pages

In this paper, we study the global properties of an SIR epidemic model with distributed delays, where there are several parallel infective stages, and some of the infected cells are detected and treated, which others remain undetected and untreated. The model is analyzed by determining a basic reproduction number $R_0$, and by using Lyapunov functionals, we prove that the infection-free equilibrium $E^0$ of system (3) is globally asymptotically attractive when $R_0\leq 1$, and that the unique infected equilibrium $E^*$ of system (3) exists and it is globally asymptotically attractive when $R_0>1$.
Figure/Table
Supplementary
Article Metrics

Citation: Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemic model with multiple parallel infectious stages. Mathematical Biosciences and Engineering, 2012, 9(3): 685-695. doi: 10.3934/mbe.2012.9.685

• 1. Jinliang Wang, Xinxin Tian, Xia Wang, Stability analysis for delayed viral infection model with multitarget cells and general incidence rate, International Journal of Biomathematics, 2016, 09, 01, 1650007, 10.1142/S1793524516500078
• 2. Xia Wang, Xinyu Song, Sanyi Tang, Libin Rong, Dynamics of an HIV Model with Multiple Infection Stages and Treatment with Different Drug Classes, Bulletin of Mathematical Biology, 2016, 78, 2, 322, 10.1007/s11538-016-0145-5
• 3. Haitao Song, Qiaochu Wang, Weihua Jiang, Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay, Journal of Applied Mathematics, 2014, 2014, 1, 10.1155/2014/929580
• 4. Xia Wang, Shengqiang Liu, Xinyu Song, A within-host virus model with multiple infected stages under time-varying environments, Applied Mathematics and Computation, 2015, 266, 119, 10.1016/j.amc.2015.05.033
• 5. Haitao Song, Shengqiang Liu, Weihua Jiang, Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate, Mathematical Methods in the Applied Sciences, 2016, 10.1002/mma.4130
• 6. Lin Zhao, Zhi-Cheng Wang, Traveling wave fronts in a diffusive epidemic model with multiple parallel infectious stages, IMA Journal of Applied Mathematics, 2016, 81, 5, 795, 10.1093/imamat/hxw033
• 7. Xia Wang, Yuefen Chen, Shengqiang Liu, Xinyu Song, A class of delayed virus dynamics models with multiple target cells, Computational and Applied Mathematics, 2013, 32, 2, 211, 10.1007/s40314-013-0004-z
• 8. Michael T. Meehan, Daniel G. Cocks, Johannes Müller, Emma S. McBryde, Global stability properties of a class of renewal epidemic models, Journal of Mathematical Biology, 2019, 10.1007/s00285-018-01324-1