Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates

Applied Mathematics and Computation

Volumn 218, Issue 8, 2011, Pages 4391-4400

  Chen, Hao ^a   Sun, Jitao ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Endemic equilibrium; Global stability; Lyapunov function; Nonlinear incidence rate; Time delay

Indexed keywords

BASIC REPRODUCTION NUMBER; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; LYAPUNOV; MULTI-GROUP; NONLINEAR INCIDENCE RATES; NUMERICAL EXAMPLE;

LYAPUNOV FUNCTIONS; TIME DELAY;

DISEASE CONTROL;

EID: 81855167021     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.10.015     Document Type: Article

References (25)

1. A. Lajmanovich, and J.A. Yorke A deterministic model for gonorrhea in a nonhomogeneous population Math. Biosci. 28 1976 221 236
2. H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 42 2000 599 653
3. E. Beretta, and V. Capasso Global stability results for a multigroup SIR epidemic model T.G. Hallam, L.J. Gross, S.A. Levin, Mathematical Ecology 1988 World Sicentific Teaneck, NJ 317 342
4. W. Huang, K.L. Cooke, and C. Castillo-Chavez Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission SIAM J. Appl. Math. 52 1992 835 854
5. H.R. Thieme Mathematics in Population Biology 2003 Princeton University Press Princeton
6. R.M. Anderson, and R.M. May Population biology of infectious diseases: Part I Nature 280 1979 361 367
7. M.Y. Li, J.R. Greaf, and J. Karasai Global dynamics of a SEIR model with varying total population size Math. Biosci. 160 1999 191 213 (Pubitemid 29398860)
8. X. Lin, and J.W.-H. So Global stability of the endemic equlibrium and uniform persistence in epidemic models with subpopulations J. Aust. Math. Soc. Ser. B 34 1993 282 295
9. H.W. Hethcote, and H.R. Thieme Stability of endemic equilibrium in epidemic models with subpopulations Math. Biosci. 75 1985 205 227 (Pubitemid 15242704)
10. D. Xiao, and S. Ruan Global analysis of an epidemic model with nonmonotone incidence rate Math. Biosci. 208 2007 419 429 (Pubitemid 47101853)
11. H. Guo, M.Y. Li, and Z. Shuai Global stability of the endemic equlibrium of multigroup SIR epidemic models Can. Appl. Math. Q. 14 2006 259 284
12. H. Guo, M.Y. Li, and Z. Shuai A graph-theoretic approach to the method of global Lyapunov functions Proc. Amer. Math. Soc. 136 2008 2793 2802
13. M.Y. Li, and Z. Shuai Global-stability problem for coupled systems of differential equations on networks J. Differ. Eqs. 248 2010 1 20
14. R.Y. Sun Global stability of the endemic equlibrium of multigroup SIR models with nonlinear incidence rate Comput. Math. Appl. 60 2010 2286 2291
15. Z.H. Yuan, and L. Wang Global stability of epidemiological models with group mixing and nonlinear incidence rates Nonlinear Anal. Real World Appl. 11 2010 995 1004
16. T.L. Zhang, J.L. Liu, and Z.D. Teng Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays Appl. Math. Comput. 214 2009 624 631
17. R. Naresh, A. Tripathi, and D. Sharma A nonlinear AIDS epidemic model with screening and time delay Appl. Math. Comput. 217 2011 4416 4426
18. C.C. McCluskey Global stability for an SIR epidemic model with delay and nonlinear incidence Nonlinear Anal. Real World Appl. 11 2010 3106 3109
19. X. Wang, Y.D. Tao, and X.Y. Song Pulse vaccination on SEIR epidemic model with nonlinear incidence rate Appl. Math. Comput. 210 2009 398 404
20. M.Y. Li, Z. Shuai, and C. Wang Global stability of multi-group epidemic models with distributed delays J. Math. Anal. Appl. 361 2010 38 47
21. P. van den Driessche, and J. Watmough Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 2002 29 48 (Pubitemid 35304346)
22. 0 in models for infectious diseases in heterogenous populations J. Math. Biol. 28 1990 365 382
23. J.P. Lasalle, The stability of Dynamical Systems, Reg. Conf. Ser. Appl. Math., SIAM, Philadelphia, 1976.
24. J.K. Hale, and S.M. Verduyn Lunel Introduction to Functional Differential Equations Appl. Math. Sci. 99 1993 Springer New York
25. H.I. Freedman, M.X. Tang, and S.G. Ruan Uniform persistence and flows near a closed positively invariant set J. Dyn. Differ. Equat. 6 1994 583 600