Mathematical Biosciences and Engineering, 2015, 12(4): 859-877. doi: 10.3934/mbe.2015.12.859.

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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

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.
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Keywords Age structure; virus dynamics model; Liapunov function; infection equilibrium; global stability.

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.

 

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