Global analysis of an SEIR model with varying population size and vaccination

Applied Mathematical Modelling

Volumn 34, Issue 10, 2010, Pages 2685-2697

  Sun, Chengjun ^a,b   Hsieh, Ying Hen ^c  

^a MCGILL UNIVERSITY   (Canada)

^b YALE UNIVERSITY   (United States)

^c CHINA MEDICAL UNIVERSITY   (Taiwan)

Author keywords

Epidemiology correlations; Global dynamics; SEIR model; Vaccination; Varying population

Indexed keywords

GLOBAL ANALYSIS; GLOBAL DYNAMICS; GLOBAL STABILITY; PARAMETER CONDITIONS; POPULATION SIZES; SEIR MODEL; THRESHOLD PARAMETERS; UNIFORM PERSISTENCE; VACCINATION STRATEGY; VARYING POPULATION SIZE;

DYNAMICS;

POPULATION STATISTICS;

EID: 77952888377     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.12.005     Document Type: Article

References (26)

1. Fenner F., Henderson D.A., Arita I., Jezek Z., Ladnyi I.D. Smallpox and Its Eradication 1998, WHO.
2. Anderson R.M., May R.M. Infectious Diseases of Humans. Dynamics and Control 1991, Oxford University Press, Oxford.
3. Garly M.A., Aaby P. The challenge of improving the efficacy of measles vaccine. Acta Tropica 2003, 85:1-17.
4. Anderson R.M., May R.M. Population biology of infectious diseases I. Nature 1979, 180:361-367.
5. http://en.wikipedia.org/wiki/Measles.
6. Brauer F. Models for the spread of universally fatal diseases. J. Math. Biol. 1990, 28:451-462.
7. Cook K.L., Van Den Driessche P. Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 1996, 35:240-260.
8. Busenberg S., Cooke K., Hsieh Y.-H. A model for HIV in Asia. Math. Biosci. 1995, 128:185-210.
9. Hsieh Y.-H., Cooke K. Behavior change and treatment of core group and bridge population: its effect on the spread of HIV/AIDS. IMA J. Math. Appl. Biol. Med. 2000, 17:213-241.
10. Sun C., Lin Y., Tang S. Global stability for a special SEIR epidemic model with nonlinear incidence rates. Chaos, Soliton. Fract. 2007, 33:290-297.
11. Feng Z. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Math. Biosci. Eng. 2007, 4:675-686.
12. Li M.Y., Wang L. Global stability in some SEIR epidemic models. IMA 2002, 126:295-311.
13. Arino J., McCluskey C.C., van den Driessche P. Global resultes for an epidemic models with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 2003, 64:260-276.
14. Yan P., Liu S. SEIR epidemic model with delay. ANZIAM J. 2006, 48:119-134.
15. Busenberg S., van den Driessche P. Analysis of a disease transmission models in a population with varying size. J. Math. Biol. 1990, 28:257-270.
16. Li M.Y., Graef J.R., Wang L., Karsai J. Global dynamics of a SEIR model with varying total population size. Math. Biosci. 1999, 160:191-213.
17. Busenberg S., Cooke K.L., Thieme H. Demographic change and persistence of HIV/AIDS in a heterogeneous population. SIAM J. Appl. Math. 1991, 54:1030-1052.
18. J.P. LaSalle, The stability of dynamical systems, in: Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
19. X. Zhao, Dynamical Systems in Population Biology, CMS books in Mathematics, Canadian Math. Soc., Springer, 2003.
20. Butler G., Waltman P. Uniformly persistent systems. Proc. Am. Math. Soc. 1986, 96:425430.
21. Usmani R.A. Applied Linear Algebra 1987, Marcel Dekker, New York.
22. Smith R.A. Some applications of Hausdorff dimension inequalities for ordinary differential equations. Proc. Roy. Soc. Edinburgh Sect. A 1986, 104:235-259.
23. Li Y., Muldowney J.S. On Bendixson's criterion. J. Differ. Equations 1993, 106:27-39.
24. H.L. Smith, Monotone dynamical systems, an introduction to the theory of competitive and cooperative systems, Am. Math. Soc., Providence, 1995.
25. Martin R.H. Logarithmic norms and projections applied to linear differential systems. J. Math. Anal. Appl. 1974, 45:432-454.
26. Hale J.K. Ordinary Differential Equations 1969, John Wiley, New York.