Propagation of HBV with spatial dependence

Mathematical Biosciences

Volumn 210, Issue 1, 2007, Pages 78-95

  Wang, Kaifa ^a,b   Wang, Wendi ^a  

^a SOUTHWEST UNIVERSITY   (China)

^b THIRD MILITARY MEDICAL UNIVERSITY   (China)

Author keywords

Diffusion; HBV; Infection; Perturbation; Waves

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; VIRUSES;

GEOMETRIC SINGULAR PERTURBATION METHODS; INFECTION; WAVE SPEED;

DISEASES;

DIFFUSION; HEPATITIS; NUMERICAL MODEL; SPATIAL VARIATION; VIRAL DISEASE;

ARTICLE; HEPATITIS B; HEPATITIS B VIRUS; MATHEMATICAL MODEL; SIMULATION; VIRUS LOAD;

HEPATITIS B; HEPATITIS B VIRUS; HEPATOCYTES; HUMANS; MATHEMATICS; MODELS, BIOLOGICAL; VIRUS REPLICATION;

HEPATITIS B VIRUS;

EID: 35248843203     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.05.004     Document Type: Article

References (42)

1. 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 chroriomeningitis virus. J. Virol. 74 (2000) 10304
2. Beasley R.P., Lin C.C., Wang K.Y., Hsieh F.J., Hwang L.Y., Stevens C.E., Sun T.S., and Szmuness W. Hepatocellular carcinoma and hepatitis B virus. Lancet 2 (1981) 1129
3. 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
4. Britton N.F. Essential Mathematical Biology (2003), Springer-Verlag, London
5. 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
6. Conley C., and Fife P. Critical manifold, travelling waves, and an example from population genetics. J. Math. Biol. 14 (1982) 159
7. Dienstag J.L., Perrillo R.P., Schiff E.R., Bartholomew M., Vicary C., and Rubin M. Double-blind, randomized, 3-month, doseranging trial of lamivudine for chronic hepatitis-B. Hepatology 20 (1994) 199
8. Doong S.L., Tsai C.H., Schinazi R.F., Liotta D.C., and Cheng Y.C. Inhibition of the replication of hepatitis B virus in vitro by 2′,3′-dideoxy-3′-thiacytidine and related analogues. Proc. Natl. Acad. Sci. USA 88 (1991) 8495
9. Dunbar S.R. Travelling wave solutions of diffusive Lotka-Volterra equations. J. Math. Biol. 17 (1983) 11
10. Faria T., Huang W., and Wu J. Travelling waves for delayed reaction-diffusion equations with global response. Proc. R. Soc. A 462 (2006) 229
11. Fenichel N. Geometric singular perturbation theory for ordinary differential equations. J. Diff. Eqns. 31 (1979) 53
12. Ferrari C., Penna A., Bertoletti A., Valli A., Antoni A.D., Giuberti T., Cavalli A., Petit M.A., and Fiaccadori F. Cellular immune response to hepatitis B virus encoded antigens in acute and chronic hepatitis B virus infection. J. Immunol. 145 (1990) 3442
13. Funka G.A., Jansen V.A.A., Bonhoeffer S., and Killingback T. Spatial models of virus-immune dynamics. J. Theor. Biol. 233 (2005) 221
14. Gourley S.A. Travelling front solutions of a nonlocal Fisher equations. J. Math. Biol. 41 (2000) 272
15. Gourley S.A., and So J.W.H. Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain. J. Math. Biol. 44 (2002) 49
16. Hartman P. Ordinary Differential Equations (1973), Wiley and Sons, Baltimore
17. Jones C.K.R.T. Geometric singular perturbation theory. In: Johnson R. (Ed). Dynamical systems. Lecture Notes in Mathematics vol. 1609 (1995), Springer, Berlin
18. Korobeinikov A. Global properties of basic virus dynamics models. Bull. Math. Biol. 66 (2004) 879
19. Kuperman M.N., and Wio H.S. Front propagation in epidemiological models with spatial dependence. Physica A 272 (1999) 206
20. Lan K.Q., and Wu J.H. Travelling wavefronts of scalar reaction-diffusion equations with and without delays. Nonlinear Anal.: Real World Appl. 4 (2003) 173
21. Maini P.K., McElwain D.L.S., and Leavesley D. Travelling waves in a wound healing assay. Appl. Math. Lett. 17 (2004) 575
22. Matzavinos A., and Chaplain M.A.J. Travelling-wave analysis of a model of the immune response to cancer. C.R. Biologies 327 (2004) 995
23. Murray J.D. Mathematical Biology (1993), Springer, Berlin, Heidelberg, New York
24. 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
25. Petrovskii S., and Shigesada N. Some exact solutions of a generalized Fisher equation related to the problem of biological invasion. Math. Biosci. 172 (2001) 73
26. Regenstein F. New approaches to the treatment of chronic viral-hepatitis-B and viral-hepatitis C. Am. J. Med. 96 (1994) 47
27. Ribeiro R.M., Lo A., and Perelson A.S. Dynamics of hepatitis B virus infection. Microbes Infect. 4 (2002) 829
28. Ruan S., and Xiao D. Stability of steady states and existence of travelling waves in a vector-disease model. Proc. R. Soc. Edinb. 134A (2004) 991
29. Shigesada N., Kawasaki K., and Teramoto E. Traveling periodic waves in heterogeneous environments. Theor. Popul. Biol. 30 (1986) 143
30. Seeger C., and Mason W.S. Hepatitis B virus biology. Microbiol. Mol. Biol. Rev. 64 (2000) 51
31. Smith H.L., and Zhao X.-Q. Traveling waves in a bio-reactor model. Nonlinear Anal.: Real World Appl. 5 (2004) 895
32. Szmolyan P. Transversal heteroclinic and homoclinic orbits in singular perturbation problems. J. Diff. Eqns. 92 (1991) 252
33. van den Bosch F., Metz J.A.J., and Diekmann O. The velocity of spatial population expansion. J. Math. Biol. 28 (1990) 529
34. Wang K., Wang W., and Liu X. Viral infection model with periodic lytic immune response. Chaos, Solitons Fractals 28 (2006) 90
35. Wang K., Wang W., and Liu X. Global stability in a viral infection model with lytic and nonlytic immune responses. Comput. Math. Appl. 51 (2006) 1593
36. Wang W., and Zhao X.-Q. An epidemic model in a patchy environment. Math. Biosci. 190 (2004) 39
37. Wang W., and Zhao X.-Q. An age-structured epidemic model in a patchy environment. SIAM J. Appl. Math. 65 (2005) 1597
38. Wang W., and Zhao X.-Q. An epidemic model with population dispersal and infection period. SIAM J. Appl. Math. 66 (2006) 1454
39. Weissberg J.I., Andres L.L., Smith C.I., Weick S., Nichols J.E., Garcia G., Robinson W.S., Merigan T.C., and Gregory P.B. Survival in chronic hepatitis B. Ann. Intern. Med. 101 (1984) 613
40. 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
41. Zhao X.-Q., and Wang W. Fisher waves in an epidemic model. Discrete Continuous Dynam. Syst. B 4 (2004) 1117
42. Zou X., and Wu J. Existence of travelling wave fronts in delayed reaction-diffusion systems via the monotone iteration method. Proc. Am. Math. Soc. 125 (1997) 2589