Global dynamics of delay epidemic models with nonlinear incidence rate and relapse

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 1, 2011, Pages 119-127

  Liu, Shengqiang ^a   Wang, Shaokai ^a   Wang, Lin ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Global stability; Infinite distributed delay; Lyapunov functions; Nonlinear incidence

Indexed keywords

DISCRETE DELAY; DISTRIBUTED DELAYS; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; LYAPUNOV; METHOD OF LYAPUNOV; NONLINEAR INCIDENCE; NONLINEAR INCIDENCE RATES;

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS;

LYAPUNOV FUNCTIONS;

EID: 77958019832     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.06.001     Document Type: Article

References (25)

1. J. Chin Control of Communicable Diseases Manual 1999 American Public Health Association Washington
2. S.W. Martin Livestock Disease Eradication: Evaluation of the Cooperative State Federal Bovine Tuberculosis Eradication Program 1994 National Academy Press Washington
3. K.E. VanLandingham, H.B. Marsteller, G.W. Ross, and F.G. Hayden Relapse of herpes simplex encephalitis after conventional acyclovir therapy JAMA 259 1988 1051 1053
4. P. van den Driessche, L. Wang, and X. Zou Modeling diseases with latency and relapse Math. Biosci. Eng. 4 2007 205 219
5. G.C. Brown, and R. Hasibuan Conidial discharge and transmission efficiency of neozygites floridana, an entomopathogenic fungus infecting two-spotted spider mites under laboratory conditions J. Invertebr. Pathol. 65 1995 10 16
6. V. Capasso, and G. Serio A generalisation of the KermackMcKendrick deterministic epidemic model Math. Biosci. 42 1978 43 61
7. S. Gao, L. Chen, J.J. Nieto, and A. Torres Analysis of a delayed epidemic model with pulse vaccination and saturation incidence Vaccine 24 2006 6037 6045
8. W.M. Liu, H.W. Hethcote, and S.A. Levin Dynamical behaviour of epidemiological models with nonlinear incidence rates J. Math. Biol. 25 1987 359 380
9. W.M. Liu, S.A. Levin, and Y. Iwasa Influence of nonlinear incidence rates upon the behaviour of SIRS epidemiological models J. Math. Biol. 23 1986 187 204
10. Z. Yuan, and L. Wang Global stability of epidemiological models with group mixing and nonlinear incidence rates Nonlinear Anal. RWA 11 2010 995 1004
11. G. Huang, Y. Takeuchi, W. Ma, D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence Rate, Bull. Math. Biol., doi:10.1007/s11538-009-9487-6.
12. M.Y. Li, and Z. Shuai Global-stability problem for coupled systems of differential equations on networks J. Differential Equations 248 2010 1 20
13. 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
14. S. Liu, and L. Wang Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy Math. Biosci. Eng. 7 2010 677 687
15. C.C. McCluskey Global stability for an SEIR epidemiological model with varying infectivity and infinite delay Math. Biosci. and Eng. 6 2009 603 610
16. C.C. McCluskey Complete global stability for an SIR epidemic model with delay-distributed or discrete Nonlinear Anal. RWA 11 2010 55 59
17. R.K. Miller Nonlinear Volterra Integral Equations 1971 W.A. Benjamin Inc. New York
18. O. Diekmann, J.A.P. Heesterbeek, and J.A.J. Metz On the definition and the computation of the basic reproduction ratio ℜ 0 in models for infectious diseases in heterogeneous populations J. Math. Biol. 28 1990 365 382
19. J.K. Hale, and J. Kato Phase space for retarded equation with infinite delay Funk. Ekv. 21 1978 11 41
20. Y. Hino, S. Murakami, and T. Naito Functional Differential Equations with Infinite Delay 1991 Springer-Verlag Germany
21. Z. Feng, W. Huang, and C. Castillo-Chavez On the role of variable latent periods in mathematical models for tuberculosis J. Dynam. Differential Equations 13 2001 425 452
22. J. Hale, and P. Waltman Persistence in infinite-dimensional systems SIAM J. Math. Anal. 20 1989 388 395
23. G. Rst, and J. Wu SEIR epidemiological model with varying infectivity and infinite delay Math. Biosci. Eng. 5 2008 389 402
24. J.K. Hale, and S.M. Verduyn Lunel Introduction to Functional Differential Equations Appl. Math. Sci. vol. 99 1993 Springer New York
25. S. Liu, and E. Beretta Stage-structured predatorprey Model with the BeddingtonDeAngelis functional response SIAM J. Appl. Math. 66 2006 1101 1129