Primary: 35L60, 92C37; Secondary: 35B35, 34K20.

Export file:

Format

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

Content

• Citation Only
• Citation and Abstract

Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function

1. School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012
2. Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250
3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Abstract    Related pages

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number $\mathcal{R}_{0}$ of the model is obtained. We investigate the global behavior of the model in terms of $\mathcal{R}_{0}$: if $\mathcal{R}_{0}\leq1$, then the infection-free equilibrium is globally asymptotically stable, whereas if $\mathcal{R}_{0}>1$, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.
Figure/Table
Supplementary
Article Metrics

Citation: Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences and Engineering, 2015, 12(4): 859-877. doi: 10.3934/mbe.2015.12.859

References

• 1. PLoS Comput. Biol., 4 (2008), e1000103, 9pp.
• 2. Math. Biosci. Eng., 10 (2013), 1335-1349.
• 3. Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
• 4. Math. Biosci., 165 (2000), 27-39.
• 5. Theoret. Pop. Biol., 56 (1999), 65-75.
• 6. J. Theoret. Biol., 190 (1998), 201-214.
• 7. SIAM. J. Appl. Math., 73 (2013), 572-593.
• 8. SIAM J. Appl. Math., 63 (2003), 1313-1327.
• 9. Mathematical Surveys and Monographs Vol 25, American Mathematical Society, Providence, RI, 1988.
• 10. SIAM J. Math. Anal., 20 (1989), 388-395.
• 11. Appl. Math. Lett., 22 (2009), 1690-1693.
• 12. Appl. Math. Lett., 24 (2011), 1199-1203.
• 13. SIAM J. Appl. Math., 70 (2010), 2693-2708.
• 14. SIAM J. Appl. Math., 72 (2012), 25-38.
• 15. J. Theoret. Biol., 185 (1997), 389-400.
• 16. Bull. Math. Biol., 58 (1996), 367-390.
• 17. Bull. Math. Biol., 72 (2010), 1492-1505.
• 18. SIAM J. Appl. Math., 70 (2010), 2434-2448.
• 19. Electron. J. Differential Equations, 65 (2001), 1-35.
• 20. Appl. Anal., 89 (2010), 1109-1140.
• 21. SIAM J. Appl. Math., 73 (2013), 1058-1095.
• 22. Commun. Pure Appl. Anal., 3 (2004), 695-727.
• 23. Math. Biosci. Eng., 9 (2012), 819-841.
• 24. Math. Biosci. Eng., 1 (2004), 267-288.
• 25. Science, 272 (1996), 74-79.
• 26. Oxford University Press, Oxford, 2000.
• 27. SIAM Rev., 41 (1999), 3-44.
• 28. SIAM. J. Appl. Math., 67 (2007), 731-756.
• 29. Differential Integral Equations, 3 (1990), 1035-1066.

• 1. Xia Wang, Yijun Lou, Xinyu Song, Age-Structured Within-Host HIV Dynamics with Multiple Target Cells, Studies in Applied Mathematics, 2017, 138, 1, 43, 10.1111/sapm.12135
• 2. Honglan Zhu, Xuebing Zhang, Dynamics and Patterns of a Diffusive Prey-Predator System with a Group Defense for Prey, Discrete Dynamics in Nature and Society, 2018, 2018, 1, 10.1155/2018/6519696
• 3. Shaoli Wang, Jiafang Zhang, Fei Xu, Xinyu Song, Dynamics of virus infection models with density-dependent diffusion and Beddington-DeAngelis functional response, Mathematical Methods in the Applied Sciences, 2017, 40, 15, 5593, 10.1002/mma.4411
• 4. Shanjing Ren, Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse, Mathematical Biosciences and Engineering, 2017, 14, 5/6, 1337, 10.3934/mbe.2017069
• 5. SHAOLI WANG, FEI XU, LIBIN RONG, BISTABILITY ANALYSIS OF AN HIV MODEL WITH IMMUNE RESPONSE, Journal of Biological Systems, 2017, 25, 04, 677, 10.1142/S021833901740006X
• 6. Eric Ávila-Vales, Erika Rivero-Esquivel, Gerardo Emilio García-Almeida, Global Dynamics of a Periodic SEIRS Model with General Incidence Rate, International Journal of Differential Equations, 2017, 2017, 1, 10.1155/2017/5796958
• 7. Jianhua Pang, Jing Chen, Zijian Liu, Ping Bi, Shigui Ruan, Local and Global Stabilities of a Viral Dynamics Model with Infection-Age and Immune Response, Journal of Dynamics and Differential Equations, 2018, 10.1007/s10884-018-9663-1
• 8. Bin Cao, Hai-Feng Huo, Hong Xiang, Global stability of an age-structure epidemic model with imperfect vaccination and relapse, Physica A: Statistical Mechanics and its Applications, 2017, 486, 638, 10.1016/j.physa.2017.05.056
• 9. Suxia Zhang, Hongbin Guo, Global analysis of age-structured multi-stage epidemic models for infectious diseases, Applied Mathematics and Computation, 2018, 337, 214, 10.1016/j.amc.2018.05.020
• 10. Chang-Yuan Cheng, Yueping Dong, Yasuhiro Takeuchi, An age-structured virus model with two routes of infection in heterogeneous environments, Nonlinear Analysis: Real World Applications, 2018, 39, 464, 10.1016/j.nonrwa.2017.07.013
• 11. Yu Yang, Yancong Xu, Global stability of a diffusive and delayed virus dynamics model with Beddington–DeAngelis incidence function and CTL immune response, Computers & Mathematics with Applications, 2016, 71, 4, 922, 10.1016/j.camwa.2016.01.009
• 12. Shaoli Wang, Xinyu Song, Global properties for an age-structured within-host model with Crowley–Martin functional response, International Journal of Biomathematics, 2017, 10, 02, 1750030, 10.1142/S1793524517500309
• 13. Shaoli Wang, Jianhong Wu, Libin Rong, A note on the global properties of an age-structured viral dynamic model with multiple target cell populations, Mathematical Biosciences and Engineering, 2016, 14, 3, 805, 10.3934/mbe.2017044
• 14. Khalid Hattaf, Yu Yang, Global dynamics of an age-structured viral infection model with general incidence function and absorption, International Journal of Biomathematics, 2018, 1850065, 10.1142/S1793524518500651
• 15. Mohamed Nor Frioui, Sofiane El-hadi Miri, Tarik Mohamed Touaoula, Unified Lyapunov functional for an age-structured virus model with very general nonlinear infection response, Journal of Applied Mathematics and Computing, 2017, 10.1007/s12190-017-1133-0
• 16. Xiangming Zhang, Zhihua Liu, Periodic oscillations in age-structured ratio-dependent predator–prey model with Michaelis–Menten type functional response, Physica D: Nonlinear Phenomena, 2018, 10.1016/j.physd.2018.10.002
• 17. Xiangming Zhang, Zhihua Liu, Hopf Bifurcation for a Susceptible-Infective Model with Infection-Age Structure, Journal of Nonlinear Science, 2019, 10.1007/s00332-019-09575-y
• 18. Zijian Liu, Chunfang Guo, Jin Yang, Hong Li, Steady States Analysis of a Nonlinear Age-Structured Tumor Cell Population Model with Quiescence and Bidirectional Transition, Acta Applicandae Mathematicae, 2020, 10.1007/s10440-019-00306-9
• 19. Wei Chen, Nafeisha Tuerxun, Zhidong Teng, The global dynamics in a wild-type and drug-resistant HIV infection model with saturated incidence, Advances in Difference Equations, 2020, 2020, 1, 10.1186/s13662-020-2497-2
• 20. Yu Yang, Lan Zou, Yasuhiro Takeuchi, Global analysis of a multi-group viral infection model with age structure, Applicable Analysis, 2020, 1, 10.1080/00036811.2020.1721471