GLOBAL STABILITY OF A VIRAL INFECTION MODEL WITH TWO DELAYS AND TWO TYPES OF TARGET CELLS

Jianquan Li; Xiuchao Song; Fengyin Gao

doi:10.11948/2012020

2012 Volume 2 Issue 3

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Jianquan Li, Xiuchao Song, Fengyin Gao. GLOBAL STABILITY OF A VIRAL INFECTION MODEL WITH TWO DELAYS AND TWO TYPES OF TARGET CELLS[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 281-292. doi: 10.11948/2012020

Citation:

Jianquan Li, Xiuchao Song, Fengyin Gao. GLOBAL STABILITY OF A VIRAL INFECTION MODEL WITH TWO DELAYS AND TWO TYPES OF TARGET CELLS[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 281-292. doi: 10.11948/2012020

GLOBAL STABILITY OF A VIRAL INFECTION MODEL WITH TWO DELAYS AND TWO TYPES OF TARGET CELLS

Faculty of Science, Air Force Engineering University, 710051 Xi'an, China

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Abstract

Abstract

In this paper, incorporating the delay of viral cytopathicity within target cells, we first presented a basic model of viral infection with delay, and then extended it into a model with two delays and two types of target cells. For the models proposed here, both their basic reproduction numbers are found. By constructing Lyapunov functionals, necessary and sufficient conditions ensuring the global stability of the models with delays are given. The obtained results show that, when the basic reproduction number is not greater than one, the infection-free equilibrium is globally stable in the feasible region, which implies that the viral infection goes extinct eventually; when it is greater than one, the infection equilibrium is globally stable in the feasible region, which implies that the viral infection persists in the body of host.
- Viral infection model /
- delay /
- equilibrium /
- global stability
MSC: 34D23;92D30

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References

[1]	D. S. Allaway and A.S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol., 64(2002), 29-64. Google Scholar
[2]	A. M. Elaim, Global properties of a class of HIV models, Nonlinear Analysis:RWA, 11(2010), 2253-3263. Google Scholar
[3]	J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. Google Scholar
[4]	H. Lerat, S. Rumin, F. Habersetzer, et al., In vivo tropism of hepatitis C virus genomic sequences in hematopoietic cells:Influence of viral load, viral genotype, and cell phenotype, Blood, 91(1998), 3841-3849. Google Scholar
[5]	F. Maggi, M. Giorgi, C. Fornai, et al., Detection and quasispecies analysis of hepatitis C virus in the cerebrospinal fluid of infected patients, J. Neurovirol., 5(1999), 319-323. Google Scholar
[6]	M. A. Nowak and R. M. May, Virus Dynamics:Mathematical Principles of Immunology and Virology, Oxford University Press, 2000. Google Scholar
[7]	M. A. Nowak, S. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas and H. McDade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93(1996), 4398-4402. Google Scholar
[8]	S. Pal, D.G. Sullivan, S. Kim, et al., Productive replication of hepatitis C virus in perihepatic lymph nodes in vivo:Implications of HCV lymphotropism, Gastroenterology, 130(2006), 1107-1116. Google Scholar
[9]	A. S. Perelson, P. Essunger, Y.Cao, M.Vesanen, A.Hurley, K.Saksela, M. Markowitz and D.D. Ho, Decay characteristics of HIV-1-infected compartments during combination therapy, Nature, 387(1997), 188-191. Google Scholar
[10]	A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41(1999), 3-44. Google Scholar
[11]	R. Qesmi, Jun Wu, Jianhong Wu, et al., Influence of backward bifurcation in a model of hepatitis B and C viruses, Math. Biosci., 224(2010), 118-125. Google Scholar
[12]	D. Sansonno, A. R. Iacobelli, V. Cornacchiulo, et al., Detection of hepatitis C virus (HCV) proteins by immunofluorescence and HCV RNA genomic sequences by non-isotopic in situ hybridization in bone marrow and peripheral blood mononuclear cells of chronically HCV-infected patients, Clin. Exp. Immunol., 103(1996), 414-421. Google Scholar
[13]	F. Verhulst, Nonlinear Differential Equations and Dynamical systems, Springer-Verlag, Berlin, Heidelberg, 1996. Google Scholar
[14]	D. Wodarz and D. N. Levy, Human immunodeficiency virus evolution towards reduced replicative fitness in vivo and the development of AIDS, Proc. R. Soc. B, 274(2007), 2481-2490. Google Scholar