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Differential Equations and Dynamical Systems

, Volume 22, Issue 2, pp 181–190 | Cite as

A Delay Virus Dynamics Model with General Incidence Rate

  • Khalid HattafEmail author
  • Noura Yousfi
  • Abdessamad Tridane
Original Research

Abstract

In this paper, the dynamical behavior of a virus dynamics model with general incidence rate and intracellular delay is studied. Lyapunov functionals are constructed and LaSalle invariance principle for delay differential equation is used to establish the global asymptotic stability of the disease-free equilibrium and the chronic infection equilibrium. The results obtained show that the global dynamics are completely determined by the value of a certain threshold parameter called the basic reproduction number \(R_0\) and under some assumptions on the general incidence function. Our results extend the known results on delay virus dynamics considered in other papers and suggest useful methods to control virus infection. These results can be applied to a variety of possible incidence functions that could be used in virus dynamics model as well as epidemic models.

Keywords

Virus dynamics General incidence rate Intracellular delay Global stability Lyapunov functional 

Notes

Acknowledgments

The authors would like to thank the anonymous referee for his/her valuable comments on the first version of the manuscript which have led to an improvement in this revised version.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2013

Authors and Affiliations

  • Khalid Hattaf
    • 1
    Email author
  • Noura Yousfi
    • 1
  • Abdessamad Tridane
    • 2
  1. 1.Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sikHassan II UniversityCasablancaMorocco
  2. 2.Department of Applied Sciences and MathematicsArizona State UniversityMesaUSA

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