Complex dynamic behavior in a viral model with delayed immune response

Physica D: Nonlinear Phenomena

Volumn 226, Issue 2, 2007, Pages 197-208

  Wang, Kaifa ^a,b   Wang, Wendi ^a   Pang, Haiyan ^a   Liu, Xianning ^a  

^a SOUTHWEST UNIVERSITY   (China)

^b THIRD MILITARY MEDICAL UNIVERSITY   (China)

Author keywords

Chaos; Delayed immune response; Periodic solutions; Stability switches

Indexed keywords

ASYMPTOTIC STABILITY; CELLS; CHAOS THEORY; NUMERICAL ANALYSIS; REAL TIME SYSTEMS; TIME SERIES ANALYSIS; VIRUSES;

DELAYED IMMUNE RESPONSE; PERIODIC SOLUTIONS; STABILITY SWITCHES;

IMMUNOLOGY;

EID: 33846645886     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.12.001     Document Type: Article

References (34)

1. Anderson R.M., and May R.M. Infectious Diseases of Humans. Dynamics and Control (1991), Oxford University, Oxford
2. Capasso V. Mathematical Structures of Epidemic Systems. Lecture Notes in Biomath. vol. 97 (1993), Springer, Heidelberg
3. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599-653
4. Kamo M., and Sasaki A. The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model. Physica D 165 (2002) 228-241
5. Wang W., and Ruan S. Simulating the SARS outbreak in Beijing with limited data. J. Theoret. Biol. 227 (2004) 369-379
6. Wang W., and Zhao X.-Q. An age-structured epidemic model in a patchy environment. SIAM J. Appl. Math. 65 (2005) 1597-1614
7. Nowak M.A., and May R.M. Virus Dynamics (2000), Cambridge University Press, Cambridge, UK
8. Tuckwell H.C., and Wan F.Y.M. On the behavior of solutions in viral dynamical models. Biosystems 73 (2004) 157-161
9. Nowak M.A., Bonhoeffer S., Hill A.M., Boehme R., and Thomas H.C. Viral dynamics in hepatitis B virus infection. Proc. Natl. Acad. Sci. USA 93 (1996) 4398-4402
10. Bonhoeffer S., May R.M., Shaw G.M., and Nowak M.A. Virus dynamics and drug therapy. Proc. Natl. Acad. Sci. USA 94 (1997) 6971-6976
11. Bartholdy C., Christensen J.P., Wodarz D., and Thomsen A.R. Persistent virus infection despite chronic cytotoxic T-lymphocyte activation in Gamma interferon-deficient mice infected with lymphocytic choriomeningitis virus. J. Virol. 74 (2000) 10304-10311
12. Wodarz D., Christensen J.P., and Thomsen A.R. The importance of lytic and nonlytic immune responses in viral infections. Trends Immunol. 23 (2002) 194-200
13. Bonhoeffer S., Coffin J.M., and Nowak M.A. Human immunodeficiency virus drug therapy and virus load. J. Virol. 71 (1997) 3275-3278
14. Nowak M.A., and Bangham C.R.M. Population dynamics of immune responses to persistent viruses. Science 272 (1996) 74-79
15. Bangham C.R.M. The immune response to HTLV-1. Curr. Opin. Immunol. 12 (2000) 397-402
16. + lymphocytes. Science 283 (1999) 857-860
17. De Boer R.J., and Perelson A.S. Towards a general function describing T cell proliferation. J. Theoret. Biol. 175 (1995) 567-576
18. De Boer R.J., and Perelson A.S. Target cell limited and immune control models of HIV infection: A comparison. J. Theoret. Biol. 190 (1998) 201-214
19. Culshaw R.V., Ruan S., and Spiteri R.J. Optimal HIV treatment by maximising immune response. J. Math. Biol. 48 (2004) 545-562
20. Iwasa Y., Michor F., and Nowak M. Some basic properties of immune selection. J. Theoret. Biol. 229 (2004) 179-188
21. Liu W.-M. Nonlinear oscillations in models of immune responses to persistent viruses. Theoret. Popul. Biol. 52 (1997) 224-230
22. Mayer H., Zaenker K.S., and an der Heiden U. A basic mathematical model of the immune response. Chaos 5 (1995) 155-161
23. Nowak M.A., and Bangham C.R.M. Population dynamics of immune responses to persistent viruses. Science 272 (1996) 74-79
24. Wodarz D. Hepatitis C virus dynamics and pathology: The role of CTL and antibody responses. J. Gen. Virol. 84 (2003) 1743-1750
25. Burić N., Mudrinic M., and Vasović N. Time delay in a basic model of the immune response. Chaos Solitons Fractals 12 (2001) 483-489
26. Canabarro A.A., Gléria I.M., and Lyra M.L. Periodic solutions and chaos in a non-linear model for the delayed cellular immune response. Physica A 342 (2004) 234-241
27. T. Kajiwara, T. Iuchi, Stability of delay differential equation models of infectious diseases in vivo, personal communication
28. Wang K., Wang W., and Liu X. Viral infection model with periodic lytic immune response. Chaos Solitons Fractals 28 (2006) 90-99
29. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, San Diego
30. Cooke K.L., and van den Driessche P. On zeros of some transcendental equations. Funkcial. Ekvac. 29 (1986) 77-90
31. Peng M., and Ucar A. The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations. Chaos Solitons Fractals 21 (2004) 883-891
32. Chun Y.K., Kim J.Y., Woo H.J., Oh S.M., Kang I., Ha J., and Kim S.S. No significant correlation exists between core promoter mutations, viral replication, and liver damage in chronic hepatitis B infection. Hepatology 32 (2000) 1154-1162
33. Deng G.-H., Wang Z.-L., Wang Y.-M., Wang K.-F., and Fan Y. Dynamic determination and analysis of serum virus load in patients with chronic HBV infection. World Chin. J. Digestol. 12 (2004) 862-865
34. Pontisso P., Bellati G., Brunetto M., Chemello L., Colloredo G., Di-Stefano R., Nicoletti M., Rumi M.G., Ruvoletto M.G., Soffredini R., Valenza L.M., and Colucci G. Hepatitis C virus RNA profiles in chronically infected individuals: Do they relate to disease activity?. Hepatology 29 (1999) 585-589