An age-structured model for the transmission dynamics of hepatitis B

SIAM Journal on Applied Mathematics

Volumn 70, Issue 8, 2010, Pages 3121-3139

  Zou, Lan ^a   Ruan, Shigui ^b   Zhang, Weinian ^a  

^a SICHUAN UNIVERSITY   (China)

^b University of Miami   (United States)

Author keywords

Age structure; Basic reproduction number; HBV; Stability; Steady state

Indexed keywords

AGE STRUCTURED MODEL; AGE STRUCTURES; BASIC REPRODUCTION NUMBER; EXISTENCE AND STABILITY; HBV; HEPATITIS B; HEPATITIS B VIRUS; NUMERICAL SIMULATION; OPTIMAL STRATEGIES; STEADY STATE; STEADY STATE SOLUTION; TRANSMISSION DYNAMICS;

VIRUSES;

EID: 78751472725     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090777645     Document Type: Article

References (32)

1. R. M. ANDERSON AND R. M. MAY, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
2. R.M. ANDERSON, R. M. MAY, AND D. J. NOKES, Preliminary analyses of the predicted impacts of various vaccination strategies on the transmission of hepatitis B virus, in The Control of Hepatitis B: The Role of Prevention in Adolescence, D. L. Bennet, ed., Gower Medical Publishing, London, 1992, 95-130.
3. S. BUSENBERG, K. COOKE, AND M. IANNELLI, Endemic thresholds and stability in a class of age-structured epidemics, SIAM J. Appl. Math., 48 (1988), 1379-1395.
4. S. N. BUSENBERG, M. IANNELLI, AND H. R. THIEME, Global behavior of an age-structured epidemic model, SIAM J. Math. Anal., 22 (1991), 1065-1080.
5. CENTERS FOR DISEASE CONTROL AND PREVENTION (CDC), The Pre-travel Consultation Travel- Related Vaccine-Preventable Diseases: Hepatitis B, in Travelers' Health-Yellow Book, Chapter 2, http://wwwn.cdc.gov/travel/yellowbook/ 2010/chapter-2/hepatitis-b.aspx.
6. 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
7. W. J. EDMUNDS, G. F. MEDLEY, AND D. J. NOKES, The transmission dynamics and control of hepatitis B virus in the Gambia, Stat. Med., 15 (1996), 2215-2233.
8. W. J. EDMUNDS, G. F. MEDLEY, AND D. J. NOKES, Vaccination against hepatitis B virus in highly endemic area: Waning vaccine-induced immunity and the need for booster doses, Trans. R. Soc. Trop. Med. Hyg., 90 (1996), 436-440.
9. W. J. EDMUNDS, G. F. MEDLEY, D. J. NOKES, A. J. HALL, AND H. C. WHITTLE, The influence of age on the development of the hepatitis B carrier state, Proc. R. Soc. Lond. B, 253 (1993), 197-201.
10. Z. FENG, W. HUANG, AND C. CASTILLO-CHAVEZ, Global behavior of a multi-group SIS epidemic model with age structure, J. Differential Equations, 218 (2005), 292-324.
11. S. T. GOLDSTEIN, F. J. ZHOU, S. C. HADLER, B. P. BELL, E. E. MAST, AND H. S. MARGOLIS, A mathematical model to estimate global hepatitis B disease burden and vaccination impact, Int. J. Epidemiol., 34 (2005), 1329-1339.
12. D. GREENHALGH, Analytical results on the stability of age-structured recurrent epidemic models, IMA J. Math. Appl. Med. Biol., 4 (1987), 109-144.
13. D. GREENHALGH, Threshold and stability results for an epidemic model with age-structured meeting rate, IMA J. Math. Appl. Med. Biol., 5 (1988), 81-100.
14. M. IANNELLI, Mathematical Theory of Age-Structured Population Dynamics, Giadini Editori e Stampatori, Pisa, 1994.
15. H. INABA, Threshold and stability results for an age-structured epidemic model, J. Math. Biol., 28 (1990), 411-434.
16. H. INABA, Mathematical analysis of an age-structured SIR epidemic model with vertical transmission, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 69-96.
17. J. D. JIA AND H. ZHUANG, The overview of the seminar on chronic hepatitis B, Chin. J. Hepatol., 12 (2004), 698-699.
18. X.-Z. LI, G. GUPUR, AND G.-T. ZHU, Threshold and stability results for an age-structured SEIR epidemic model, Comput. Math. Appl., 42 (2001), 883-907.
19. G.-T. LIU, C.-W. SI, Q.-H. WANG, L.-H. CHEN, H.-S. CHEN, D.-Z. XU, L.-X. ZHANG, B.-E. WANG, L.-T. WANG, AND Y. LI, Comments on the prevention and research of chronic hepatitis in China, Natl. Med. J. China, 82 (2002), 74-76.
20. M. MARTCHEVA AND G. CRISPINO-O'CONNELL, The transmission of meningococcal infection: A mathematical study, J. Math. Anal. Appl., 283 (2003), 251-275.
21. A. R. MCLEAN AND B. S. BLUMBERG, Modelling the impact of mass vaccination against hepatitis B. I. Model formulation and parameter estimation, Proc. R. Soc. Lond. B, 256 (1994), 7-15.
22. A. MCKENDRICK, Applications of mathematics to medical problems, Proc. Edinb. Math. Soc., 44 (1926), 98-130.
23. G. F. MEDLEY, N. A. LINDOP, W. J. EDMUNDS, AND D. J. NOKES, Hepatitis-B virus endemicity: Heterogeneity, catastrophic dynamics and control, Nat. Med., 7 (2001), 619-624.
24. MINISTRY OF HEALTH OF THE PEOPLE'S REPUBLIC OF CHINA (MOHC), 2009, http://www.moh. gov.cn/publicfiles//business/htmlfiles/zwgkzt/pyq/list.htm.
25. F. SHARPE AND A. LOTKA, A problem in age-distribution, Philos. Mag., 6 (1911), 435-438.
26. C. W. SHEPARD, E. P. SIMARD, L. FINELLI, A. E. FIORE, AND B. P. BELL, Hepatitis B virus infection: Epidemiology and vaccination, Epidemiol. Rev., 28 (2006), 112-125.
27. G. F. WEBB, Population models structured by age, size, and spatial position, in Structured Population Models in Biology and Epidemiology, P. Magal and S. Ruan, eds., Lecture Notes in Math. 1936, Springer-Verlag, Berlin, New York, 2008, 1-49.
28. J. R. WILLIAMS, D. J. NOKES, G. F. MEDLEY, AND R. M. ANDERSON, The transmission dynamics of hepatitis B in the UK: A mathematical model for evaluating costs and effectiveness of immunization programmes, Epidemiol. Infect., 116 (1996), 71-89.
29. WORLD HEALTH ORGANIZATION (WHO), Expanded programme on immunization: Global Advisory Group, Part I, Weekly Epidemiological Record, 67 (1992), 11-19.
30. WORLD HEALTH ORGANIZATION (WHO), Hepatitis B, Revised August 2008, http://www.who. int/mediacentre/factsheets/fs204/en/index.html.
31. S.-J. ZHAO, Z.-Y. XU, AND Y. LU, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. Epidemiol., 29 (2000), 744-752.
32. L. ZOU, W. ZHANG, AND S. RUAN, Modelling the transmission dynamics and control of Hepatitis B virus in China, J. Theoret. Biol., 262 (2010), 330-338.