Global stability of a stage-structured epidemic model with a nonlinear incidence

Applied Mathematics and Computation

Volumn 214, Issue 1, 2009, Pages 73-82

  Cai, Li Ming ^a,b   Li, Xue Zhi ^a   Ghosh, Mini ^c  

^a XINYANG NORMAL UNIVERSITY   (China)

^b CHINESE ACADEMY OF SCIENCES   (China)

^c THAPAR UNIVERSITY   (India)

Author keywords

Epidemic model; Global stability; Stage structure

Indexed keywords

ANALYTICAL RESULTS; BASIC REPRODUCTION NUMBER; DISEASE-FREE EQUILIBRIUM; DYNAMIC BEHAVIORS; ENDEMIC EQUILIBRIUM; EPIDEMIC MODEL; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; LIMIT THEORY; NONLINEAR INCIDENCE; NUMERICAL SIMULATION; STAGE STRUCTURE;

ASYMPTOTIC ANALYSIS; STRUCTURES (BUILT OBJECTS);

DISEASE CONTROL;

EID: 67349249710     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.03.088     Document Type: Article

References (34)

1. Anderson R.M., and May R.M. Infectious Diseases of Humans (1991), Oxford University Press, London
2. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599-653
3. Levin S.A., Hallam T.G., and Gross L.J. Applied Mathematical Ecology (1989), Springer, New York
4. Velasco-Hernandez J.X. An epidemiological model for the dynamics of Chagas' disease. BioSystems 26 (1991) 127-134
5. Hyman J.M., Li J., and Stanley E.A. The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci. 155 (1999) 77-109
6. Guo H., and Li M.Y. Global dynamics of a staged progression model for infectious diseases. Math. Biosci. Eng. 3 (2006) 513-525
7. Li J., Zhou Y., Ma Z., and Hyman J.M. Epidemiological models for mutating pathogens. SIAM J. Appl. Math. 65 (2004) 1-23
8. Martcheva M., and Castillo-Chavez C. Disease with chronic stage in a population with varying size. Math. Biosci. 182 (2003) 1-25
9. Moghadas S.M., and Gumel A.B. Global stability of a two-stage epidemic model with generalized non-linear incidence. Math. Comput. Simulat. 60 (2002) 107-118
10. Martcheva M., and Castillo-Chavez C. Diseases with chronic stage in a population with varying size. Math. Biosci. 182 (2003) 1-25
11. Ma Z., Zhou Y., Wang W., and Jin Z. Mathematical Models and Dynamics of Infectious Diseases (2004), China Sciences Press, Beijing
12. Liu W.M., Hethcote H.W., and Levin S.A. Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 25 (1987) 359-380
13. 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
14. Wilson E.B., and Worcester J. The law of mass action in epidemiology. Proc. Natl. Acad. Sci. USA 31 1 (1945) 24-34
15. Wilson E.B., and Worcester J. The law of mass action in epidemiology II. Proc. Natl. Acad. Sci. USA 31 4 (1945) 109-116
16. Yorke J.A., and London W.P. Recurrent outbreaks of measles, chickenpox and mumps II. Am. J. Epidemiol. 98 (1973) 469-482
17. d'Onofrio A. Biomathematical analysis and extension of the new class of epidemic models proposed by Satsuma et al. (2004). Appl. Math. Comput. 170 (2005) 125-134
18. Hethcote H.W., and van den Driessche P. Some epidemiological models with nonlinear incidence. J. Math. Biol. 29 (1991) 271-287
19. Ruan S., and Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differ. Equat. 188 (2003) 135-163
20. van den Driessche P., and Watmough J. A simple SIS epidemic model with a backward bifurcation. J. Math. Biol. 40 (2000) 525-540
21. Alexander M.E., and Moghadas S.M. Periodicity in an epidemic model with a generalized nonlinear incidence. Math. Biosci. 189 (2004) 75-96
22. Li M.Y., and Muldowney J.S. Global stability for the SEIR model in epidemiology. Math. Biosci. 125 (1995) 155-164
23. Dulac H. Recherche des cycles limites. C.R. Math. Acad. Sci. Paris 204 (1973) 1703-1706
24. Li M.Y., and Muldowney J.S. A geometric approach to global-stability problems. SIAM J. Math. Anal. 27 (1996) 1070-1083
25. Li M.Y., and Muldowney J.S. On Bendixsons criterion. J. Differ. Equat. 106 (1993) 27-39
26. Li M.Y., Muldowney J.S., and van den Driessche P. Global stability of SEIRS models in epidemiology. Can. Appl. Math. Quart. 7 4 (1999) 409-425
27. Li M.Y., Smith H.L., and Wang L. Global dynamics of an SEIR epidemic model with vertical transmission. SIAM J. Appl. Math. 62 1 (2001) 58-69
28. Busenberg S., and van den Driessche P. Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 28 (1990) 257-270
29. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29-48
30. McCluskey C.C., and van den Driessche P. Global analysis of two tuberculosis models. J. Dynam. Differ. Equat. 16 (2004) 139-166
31. Feng Z., Iannelli M., and Milner F. A two-strain tuberculosis model with age of infection. SIAM J. Appl. Math. 62 (2002) 1634-1656
32. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 2 (1993) 407-435
33. Li J., and Ma Z. Qualitative analyses of SIS epidemic model with vaccination varying total population. Math. Comput. Model. 35 (2002) 1235-1243
34. Perko L. Differential Equations and Dynamical Systems. second ed. (1998), Springer-Verlag, New York