Travelling waves of a hepatitis B virus infection model with spatial diffusion and time delay

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 75, Issue 3, 2010, Pages 392-417

  Gan, Qintao ^a   Xu, Rui ^a   Yang, Pinghua ^a   Wu, Zheng ^b  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b BETHUNE INTERNATIONAL PEACE HOSPITAL   (China)

Author keywords

HBV; partial monotonicity; reaction diffusion; travelling waves; upper lower solutions

Indexed keywords

CHARACTERISTIC EQUATION; DISCRETE TIME DELAY; HEPATITIS B VIRUS INFECTION; INCUBATION PERIODS; ITERATION METHOD; LOCAL STABILITY; MONOTONICITY; NEUMANN BOUNDARY CONDITION; NUMERICAL SIMULATION; REACTION DIFFUSION; SCHAUDER'S FIXED POINT THEOREM; SPATIAL DIFFUSIONS; STEADY STATE; TRAVELLING WAVES; UPPER-LOWER SOLUTION;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFUSION IN LIQUIDS; TIME DELAY; VIRUSES;

WAVE TRANSMISSION;

EID: 77955124495     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxq009     Document Type: Article

References (25)

1. BEASLEY, R. P., LIN, C. C., HWANG, L. Y. & CHIEN, C. S. (1981) Hepatocellular carcinoma and hepatitis B virus. Lancet, 2, 1129-1133.
2. GE, Z. & HE, Y. (2009) Traveling wavefronts for a two-species predator-prey system with diffusion terms and stage structure. Appl. Math. Model., 33, 1356-1365.
3. GOURLEY, S. A. & SO, J. W. H. (2002) Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain. J. Math. Biol., 44, 49-78.
4. HERZ, A. V. M., BONHOEFFER, S., ANDERSON, R. M., MAY, R. M. & NOWAK, M. A. (1996) Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. Proc. Natl. Acad. Sci. USA, 93, 7247-7251. (Pubitemid 26243534)
5. HUANG, J. & ZOU, X. (2002) Traveling wavefronts in diffusive and cooperative Lotka-Volterra system with delays. J. Math. Anal. Appl., 271, 455-466.
6. HUANG, J. & ZOU, X. (2006) Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity. Acta Math. Appl. Sin., 22, 243-256. (Pubitemid 43536214)
7. JACQUEZ, J. Z. & SIMON, C. P. (2002) Qualitative theory of compartmental systems with lags. Math. Biosci., 180, 329-362.
8. LI, W., LIN, G. & RUAN, S. (2006) Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems. Nonlinearity, 19, 1253-1273. (Pubitemid 43752404)
9. MA, S. (2001) Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. J. Differ. Equ., 171, 294-314. (Pubitemid 33377852)
10. MURRAY, J. M. (2002) Mathematical Biology, I: An Introduction, 3rd edn. New York: Springer.
11. MURRAY, J. M. (2003) Mathematical Biology, II: Spatial Models and Biomedical Applications, 3rd edn. New York: Springer.
12. NELSON, P. W., MURRAY, J. M. & PERELSON, A. S. (2000) A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci., 163, 201-215.
13. NOWAK, M. A., BONHOEFFER, S., HILL, A. M., BOEHME, R., THOMAS, H. C. & MCDADE, H. (1996) Viral dynamics in hepatitis B virus infection. Proc. Natl. Acad. Sci. USA, 93, 4398-4402. (Pubitemid 26144299)
14. NOWAK, M. A. & MAY, R. M. (2000) Virus Dynamics. New York: Oxford University Press.
15. SCHAAF, K. W. (1987) Asymptotic behavior and travelling wave solutions for parabolic functional differential equations. Trans. Am. Math. Soc., 302, 587-615.
16. SEEGER, C. & MASON, W. S. (2000) Hepatitis B virus biology. Microbiol. Mol. Biol. Rev., 64, 51-68. (Pubitemid 30143840)
17. WANG, K. & WANG, W. (2007) Propagation of HBV with spatial dependence. Math. Biosci., 210, 78-95. (Pubitemid 47562489)
18. WANG, K., WANG, W. & SONG, S. (2008) Dynamics of an HBV model with diffusion and delay. J. Theor. Biol., 253, 36-44.
19. WEISSBERG, J. I., ANDRES, L. L., SMITH, C. I., WEICK, S., NICHOLS, J. E., GARCIA, G., ROBINSON, W. S., MERIGAN, T. C. & GREGORY, P. B. (1984) Survival in chronic hepatitis B. An analysis of 379 patients. Ann. Intern. Med., 101, 613-616. (Pubitemid 15223297)
20. WU, J. (1996) Theory and Applications of Partial Functional Differential Equations. New York: Springer.
21. WU, J. & ZOU, X. (2001) Travelling wave fronts of reaction diffusion systems with delay. J. Dyn. Differ. Equ., 13, 651-687. (Pubitemid 33808772)
22. XU, R., CHAPLAIN, M. A. J. & DAVIDSON, F. A. (2006) Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays. Chaos Solitons Fractals, 30, 974-992. (Pubitemid 43913484)
23. XU, R. & MA, Z. (2009) An HBV model with diffusion and time delay. J. Theor. Biol., 257, 499-509.
24. ZEIDLER, E. (1986) Nonlinear Functional Analysis and Its Applications, I, Fixed-point Theorems. New York: Springer.
25. ZOU, X. & WU, J. (1998) Local existence and stability of periodic traveling wave of lattice functional differential equations. Can. Appl. Math. Q., 6, 397-418.