GLOBAL ANALYSIS FOR A DELAY - DISTRIBUTED VIRAL INFECTION MODEL WITH ANTIBODIES AND GENERAL NONLINEAR INCIDENCE RATE

다국어 초록 (Multilingual Abstract)

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R0 (the basic infection reproduction number) and R1 (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle’s invariance principle.

목차 (Table of Contents)

• ABSTRACT
• 1. INTRODUCTION
• 2. THE MATHEMATICAL MODEL
• 3. NON-NEGATIVITY AND BOUNDEDNESS OF SOLUTIONS
• 4. THE EQUILIBRIA AND THRESHOLD PARAMETERS
• 5. GLOBAL STABILITY ANALYSIS
• 6. CONCLUSION
• REFERENCES

참고문헌 (Reference)

1 M. A. Nowak, "Virus dynamics: Mathematical Principles of Immunology and Virology" Oxford Uni. 2000

2 P. Tanvi, "Virus antibody dynamics in primary and secondary dengue infections"

3 W. Dominik, "The role of antigen-independent persistence of memory cytotoxic T lymphocytes" 12 (12): 467-477, 2000

4 S. Eikenberry, "The dynamics of a delay model of HBV infection with logistic hepatocyte growth" 6 : 283-299, 2009

5 M. A . Obaid, "Stability of virus infection models with antibodies and chronically infected cells" 2014

6 A. Murase, "Stability analysis of pathogen-immune interaction dynamics" 51 : 247-267, 2005

7 K. Hattaf, "Stability analysis of a virus dynamics model with general incidence rate and two delays" 221 : 514-521, 2013

8 M. A. Nowak, "Population dynamics of immune responses to persistent viruses" 272 : 74-79, 1996

9 M. A. Nowak, "Population dynamics of immune responses to persistent viruses" 272 : 74-79, 1996

10 Y. Zhao, "Mathematical insights in evaluating state dependent e ectiveness of HIV prevention interventions" 75 : 649-675, 2013

11 L. Wang, "Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells" 200 (200): 44-57, 2006

12 P. W. Nelson, "Mathematical analysis of delay differential equation models of HIV-1 infection" 179 : 73-94, 2002

13 K. Hattaf, "Mathematical analysis of a virus dynamics model with general incidence rate and cure rate" 13 : 1866-1872, 2012

14 A. S. Perelson, "Mathematical analysis of HIV-1 dynamics in vivo" 41 : 3-44, 1999

15 G. Huang, "Lyapunov functionals for delay differential equations model of viral infection" 70 : 2693-2708, 2010

16 P. K. Roy, "Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model" 14 : 1621-1633, 2013

17 J. K. Hale, "Introduction to functional differential equations" Springer-Verlag 1993

18 J. Mittler, "Influence of delayed virus production on viral dynamics in HIV-1 infected patients" 152 : 143-163, 1998

19 R. Qesmi, "Influence of backward bifurcation in a model of hepatitis B and C viruses" 224 : 118-125, 2010

20 J. A. Deans, "Immunology of malaria" 37 : 25-49, 1983

21 A. U. Neumann, "Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy" 282 : 103-107, 1998

22 D. S. Callaway, "HIV-1 infection and low steady state viral loads" 64 : 29-64, 2002

23 S. Wang, "Global stability of in host viral models with humoral immunity and intracellular delays" 36 : 1313-1322, 2012

24 K. Hattaf, "Global stability of a virus dynamics model with cure rate and absorption" 22 : 386-389, 2014

25 Ahmed Elaiw, "Global stability of HIV infection models with intracellular delays" 대한수학회 49 (49): 779-794, 2012

26 T.Wang, "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity" 89 : 13-22, 2013

27 A. M. Elaiw, "Global properties of virus dynamics models with multitarget cells and discrete-time delays" 2011

28 A. Korobeinikov, "Global properties of infectious disease models with nonlinear incdence" 69 : 1871-1886, 2007

29 A. M. Elaiw, "Global properties of a class of virus infection models with multitarget cells" 69 : 423-435, 2012

30 A. M. Elaiw, "Global properties of a class of HIV models" 11 : 2253-2263, 2010

31 A.M. Elaiw, "Global properties of a class of HIV infection models with Beddington-DeAngelis functional response" 36 : 383-394, 2013

32 A. M. Elaiw, "Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays" 7 (7): 25-, 2014

33 A. M. Elaiw, "Global dynamics of virus infection model with antibody immune response and distributed delays" 2013 : 2013

34 A. M. Elaiw, "Global dynamics of an HIV infection model with two classes of target cells and distributed delays" 2012 : 2012

35 M. Y. Li, "Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response" 13 : 1080-1092, 2012

36 N. Bairagi, "Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay"

37 A. M. Elaiw, "Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages" 2013

38 S. A. Gourley, "Dynamics of a delay differential equation model of hepatitis B virus infection" 2 : 140-153, 2008

39 J. Li, "Dynamical behaviors of an HBV infection model with logistic hepatocyte growth" 54 : 704-711, 2011

40 N. M. Dixit, "Complex patterns of viral load decay under antiretroviral therapy: Influence of pharmacokinetics and intracellular delay" 226 : 95-109, 2004

41 H. F. Huo, "A virus dynamics model with saturation infection and humoral immunity" 6 : 1977-1983, 2012

42 P. W. Nelson, "A model of HIV-1 pathogenesis that includes an intracellular delay" 163 : 201-215, 2000

43 R. Qesmi, "A hepatitis B and C virus model with age since infection that exhibit backward bifurcation" 71 (71): 1509-1530, 2011

44 A. M. Elaiw, "A delayed viral infection model with antibody immune response" 10 (10): 695-700, 2013

45 R. V. Culshaw, "A delay-differential equation model of HIV infection of CD4+ T-cells" 165 : 27-39, 2000

46 K. Hattaf, "A delay virus dynamics model with general incidence rate" 22 (22): 181-190, 2014

47 X. Wang, "A class of delayed viral models with saturation infection rate and immune response" 36 : 125-142, 2013