Dynamical behavior for a stage-structured SIR infectious disease model

Nonlinear Analysis: Real World Applications

Volumn 3, Issue 2, 2002, Pages 175-190

  Xiao, Yanni ^a,b   Chen, Lansun ^a   Ven Den Bosch, Frank ^b  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b IACR Rothmasted ^*  (United Kingdom)

Author keywords

Globally asymptotically stable; SIR infectious disease; Stage structure; Time delay

Indexed keywords

EID: 0142243570     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(01)00021-9     Document Type: Article

References (14)

1. W.G. Aiello, H.I. Freedman, A time delay model of single-species growth with stage structure, Math. Biosci. 101 (1990) 139-153.
2. W.G. Aiello, H.I. Freedman, J. Wu, Analysis of a model representing stage structured population growth with state-dependent time delay, SIAM J. Appl. Math. 52 (1992) 855-869.
3. M.G. Bulmer, Periodical insects, Amer. Nat. 111 (1977) 1099-1117.
4. L.S. Chen, Mathematical Models and Methods in Ecology, Science Press, Beijing, 1988.
5. L.S. Chen, J. Chen, Nonlinear Dynamical System in Biology, Science Press, Beijing, 1993.
6. R.A. Desharnais, L. Liu, Stable demographic limit cycles in a laboratory populations of tribolium castaneum, J. Anim. Ecol. 56 (1987) 885-906.
7. L. Esteva, C. Vargas, A model for dengue disease with variable human population, J. Math. Biol. 38 (1999) 220-240.
8. M.E. Fisher, B.S. Goh, Stability results for delayed-recruitment models in population dynamics, J. Math. Biol. 19 (1990) 139-153.
9. H.W. Hethcote, H.W. Stesh, P. Van Den Driessche, Nonlinear oscillations in epidemic models, SIAM J. Appl. Math. 40 (1981) 1-9.
10. H.W. Hethcote, H.W. Stech, P. Van Den Driessche, Stability analysis for models of diseases without immunity, J. Math. Biol. 13 (1981) 185-198.
11. J.H. Swart, Hopf bifurcation and stable limit cycle behavior in the spread of infectious disease, with special appriation to fox rabies, Math. Biosci. 95 (1989) 199-207.
12. K. Tognetti, The two stage stochastic model, Math. Biosci. 25 (1975) 195-204.
13. W.D. Wang, L.S. Chen, A predator-prey system with stage-structure for predator, Comput. Math. Appl. 33 (1997) 83-91.
14. S.N. Wood, S.P. Blythe, W.S. Curney, R.M. Nisbet, Instability in mortality estimation schemes related to stage structure population models, IMA J. Math. Appl. Med. Biol. 6 (1989) 47-68.