The effect of constant and mixed impulsive vaccination on SIS epidemic models incorporating media coverage

Rocky Mountain Journal of Mathematics

Volumn 38, Issue 5, 2008, Pages 1437-1455

  Li, Yongfeng ^a   Ma, Chaoqun ^b   Cui, Jingan ^a  

^a NANJING NORMAL UNIVERSITY   (China)

^b HUNAN UNIVERSITY   (China)

Author keywords

Impulsive effect; Media coverage; Vaccination; Vertical transmission

Indexed keywords

EID: 58049146039     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/RMJ-2008-38-5-1437     Document Type: Conference Paper

References (16)

1. S. Busenberg and K. Cook, Vertically transmitted disease, Models and Dynamics, Biomathematics 23, Springer-Verlag, Berlin, 1993.
2. S.N. Busenberg and K.L. Cooke, Models of vertical transmitted diseases with sequential-continuous dynamics, in Nonlinear phenomena in mathematical sciences, V. Lakshmicantham, ed., Academic Press, New York, 1982.
3. K.L. Cook and S.N. Busenberg, Vertical transmission diseases, in Nonlinear phenomena in mathematical sciences, V. Lakshmicantham, ed., Academic Press, New York, 1982.
4. J. Cui, Y. Sun and H. Zhu, The impact of media on the spreading and control of infectious disease, J. Dyn. Differ. Equations, http://www.springerlink.com/content/n3068q3428wnj165/.
5. A. d'Onofrio, Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures, Math. Comput. Model. 36 (2002), 473-489.
6. -, Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times, Appl. Math. Comput. 151 (2004), 181-187.
7. P.M. Fine, Vectors and vertical transmission, an epidemiological perspective, Annals New York Acad. Sci. 266 (1975), 173-194.
8. P.M. Fine and J.W. Leduc, Towards a quantitative understanding of the epidemiology of Keystone virus in the eastern United States, Amer. J. Tropical Med. Hygiene 27 (1978), 322-338.
9. J. Hui and D.M. Zhu, Global stability and periodicity on SIS epidemic models with backward bifurcation, Comput. Math. Appl. 50 (2005), 1271-1290.
10. V. Lakshmikantham, D.D. Bainov and P.S.Simeonov, Theory of impulsive differential equations, World Scientific, Singapore, 1989.
11. W.M. Liu, H.W. Hethcote and S.A.Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, J. Math. Biol. 25 (1987), 359-380.
12. W.M. Liu, S.A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol. 23 (1986), 187-204.
13. R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious disease, preprint.
14. Z. Lu, X. Chi and L. Chen, The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission, Math. Comput. Model. 36 (2002), 1039-1057.
15. B. Shulgin, L. Stone and Z.Agur, Theoretical examination of pulse vaccination policy in the SIR epidemic model, Math. Comput. Model. 31(2000), 207-215.
16. J.A. Yorke and W.P. London, Recurrent outbreaks of measles, chickenpox and mumps II, Amer. J. Epidemiology 98 (1973), 469-482.