Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 2, 2009, Pages 565-575

  Zhang, Xu ^a,b   Liu, Xianning ^a  

^a SOUTHWEST UNIVERSITY   (China)

^b CHONGQING NORMAL UNIVERSITY   (China)

Author keywords

Backward bifurcation; Global stability; SIS; Treatment

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; SURVEYING INSTRUMENTS; SWITCHING CIRCUITS;

BACKWARD BIFURCATION; BASIC REPRODUCTION NUMBERS; BISTABLE; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; INCIDENCE RATES; NONLINEAR INCIDENCE RATES; SIS; TREATMENT;

DISEASE CONTROL;

EID: 56549115873     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.10.011     Document Type: Article

References (20)

1. In: Anderson R.M., and May R.M. (Eds). Population Biology of Infectious Diseases (1982), Springer-Verlag, Berlin, Heidelberg, New York
2. In: Anderson R.M., and May R.M. (Eds). Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University, Oxford
3. Arino J., McCluskey C.C., and van den Driessche P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 64 (2003) 260-276
4. Castillo-Chavez C., and Thieme H.R. Asymptotically autonomous epidemic models. In: Arino O., et al. (Ed). Mathematical Population Dynamics: Analysis of Heterogeneity. Theory of Epidemics vol. I (1995), Wuerz, Canada 33-50
5. Diekmann O., and Heesterbeek J.A.P. Mathematical epidemiology of infectious diseases. Model Building, Analysis and Interpretation. Wiley Series in Mathematical and Computational Biology (2000), John Wiley and Sons, Chichester
6. Dushoff J., Huang W., and Castillo-Chavez C. Backwards bifurcations and catastrophe in simple models of fatal diseases. J. Math. Biol. 36 (1998) 227-248
7. Hadeler K.P., and van den Driessche P. Backward bifurcation in epidemic control. Math. Biosci. 146 (1997) 15-35
8. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599-653
9. Li G., Wang W., Wang K., and Jin Z. Dynamic behavior of a parasite-host model with general incidence. J. Math. Anal. Appl. 331 (2007) 631-643
10. Lizana M., and Rivero J. Multiparametric bifurcations for a model in epidemiology. J. Math. Biol. 35 (1996) 21-36
11. Liu W.M., Levin S.A., and Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23 (1986) 187-204
12. Martcheva M., and Thieme H.R. Progression age enhanced backward bifurcation in an epidemic model with superinfection. J. Math. Biol. 46 (2003) 385-424
13. Ruan S., and Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differential Equations 188 (2003) 135-163
14. Takeuchi Y., Liu X., and Cui J. Global dynamics of SIS models with transport-related infection. J. Math. Anal. Appl. 329 (2007) 1460-1471
15. Takeuchi Y., Ma W., and Beretta E. Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear Anal. 42 (2000) 931-947
16. Thieme H.R. Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30 (1992) 755-763
17. van den Driessche P., and Watmough J. A simple SIS epidemic model with a backward bifurcation. J. Math. Biol. 40 (2000) 525-540
18. Wang W. Backward bifurcation of an epidemic model with treatment. Math. Biosci. 201 (2006) 58-71
19. Wang W., and Ma Z. Global dynamics of an epidemic model with time delay. Nonlinear Anal. RWA 3 (2002) 365-373
20. Ye Y., et al. Theory of Limit Cycles. Trans. Math. Monogr. vol. 66 (1986), AMS, Providence