Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination

Applied Mathematics and Mechanics (English Edition)

Volumn 28, Issue 9, 2007, Pages 1259-1271

  Meng, Xin Zhu ^a,b   Chen, Lan Sun ^b   Song, Zhi Tao ^a  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Delays; Global attractivity; Horizontal and vertical transmission; Permanence; Pulse vaccination

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; VACCINES;

DYNAMICS BEHAVIORS; HORIZONTAL AND VERTICAL TRANSMISSION; PULSE VACCINATION;

DISEASES;

EID: 38049132370     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-007-0914-x     Document Type: Article

References (28)

1. Michael Y Li, Gaef John R, Wang Liancheng, et al. Global dynamics of a SEIR model with varying total population size[J]. Mathematical Biosciences, 1999, 160(2):191-213.
2. Michael Y Li, Hall Smith, Wang Liancheng. Global dynamics of an SEIR epidemic model with vertical transmission[J]. SIAM Journal on Applied Mathematics, 2001, 62(1):58-69.
3. Al-Showaikh FNM, Twizell E H. One-dimensional measles dynamics[J]. Applied Mathematics and Computation, 2004, 152(1):169-194.
4. Greenhalgh D. Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity[J]. Mathematical and Computer Modelling, 1997, 25(5):85-107.
5. Li Guihua, Jin Zhen. Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period[J]. Chaos, Solitons and Fractals, 2005, 25(5):1177-1184.
6. Hethcote H W, Stech H W, van den Driessche P. Periodicity and stability in epidemic models: a survey[M]. In: Differential Equations and Applications in Ecology, Epidemics, and Population Problems, New York: Academic Press, 1981, 65-85.
7. d'Onofrio Alberto. Stability properties of pulse vaccination strategy in SEIR epidemic model[J]. Mathematical Biosciences, 2002, 179(1):57-72.
8. d'Onofrio Alberto. Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times[J]. Applied Mathematics and Computation, 2004, 151(1):181-187.
9. Fine P M. Vectors and vertical transmission: an epidemiologic perspective[J]. Annals of the New York Academy of Sciences, 1975, 266(11):173-194.
10. Busenberg S, Cooke K L, Pozio M A. Analysis of a model of a vertically transmitted disease[J]. Journal of Mathematical Biology, 1983, 17(3):305-329.
11. Busenberg S N, Cooke K L. Models of vertical transmitted diseases with sequenty-continuous dynamics[M]. In: Lakshmicantham V (ed). Nonlinear Phenomena in Mathematical Sciences, New York: Academic Press, 1982, 179-187.
12. Cook K L, Busenberg S N. Vertical transmission diseases[M]. In: Lakshmicantham V (ed). Nonlinear Phenomena in Mathematical Sciences, New York: Academic Press, 1982, 189.
13. Lu Zhonghua, Chi Xuebin, Chen Lansun. The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission[J]. Mathematical and Computer Modelling, 2002, 36(9):1039-1057.
14. d'Onofrio Alberto. On pulse vaccination strategy in the SIR epidemic model with vertical transmission[J]. Applied Mathematics Letters, 2005, 18(7):729-732.
15. Nokes D, Swinton J. The control of childhood viral infections by pulse vaccination[J]. IMA Journal Mathematics Applied Biology Medication, 1995, 12(1):29-53.
16. Zeng Guangzhao, Chen Lansun. Complexity and asymptotical behavior of a SIRS epidemic model with proportional implse vaccination[J]. Advances in Complex Systems, 2005, 8(4):419-431.
17. van den Driessche P, Watmough J. A simple SIS epidemic model with a backward bifurcation[J]. Journal of Mathematical Biology, 2000, 40(6):525-540.
18. van den Driessche P, Watmough J. Epidemic solutions and endemic catastrophes[J]. Fields Institute Communications, 2003, 36(1):247-257.
19. Alexander M E, Moghadas S M. Periodicity in an epidemic model with a generalized non-linear incidence[J]. Mathematical Biosciences, 2004, 189(1):75-96.
20. Takeuchi Yasuhiro, Ma Wanbiao, Beretta Edoardo. Global asymptotic properties of a delay SIR epidemic model with finite incubation times[J]. Nonlinear Analysis, 2000, 42(6):931-947.
21. Ma Wanbiao, Song Mei, Takeuchi Yasuhiro. Global stability of an sir epidemic model with time delay[J]. Applied Mathematics Letters, 2004, 17(10):1141-1145.
22. Jin Zhen, Ma Zhien. The stability of an SIR epidemic model with time delays [J]. Mathematical Biosciences and Engineering, 2006, 3(1):101-109.
23. Beretta Edoardo, Hara Tadayuki, Ma Wangbao, et al. Global asymptotic stability of an SIR epidemic model with distributed time delay[J]. Nonlinear Analysis, 2001, 47(6):4107-4115.
24. Lakshmikantham V, Bainov D, Simeonov P. Theory of impulsive differential equations[M]. Singapore: World Scientific, 1989.
25. Liu Xinzhi, Teo Kok Lay, Zhang Yi. Absolute stability of impulsive control systems with time delay[J]. Nonlinear Analysis, 2005, 62(3):429-453.
26. Kuang Yang. Delay differential equations with applications in population dynamics[M]. San Diego, CA: Academic Press, INC, 1993.
27. Cooke K L, van den Driessche P. Analysis of an SEIRS epidemic model with two delays[J]. Journal of Mathematical Biology, 1996, 35(2):240-260.
28. Wang Wendi. Global behavior of an SEIRS epidemic model with time delays[J]. Applied Mathematics Letters, 2002, 15(4):423-428.