Dynamical behavior of a vector-host epidemic model with demographic structure

Computers and Mathematics with Applications

Volumn 56, Issue 12, 2008, Pages 3118-3129

  Qiu, Zhipeng ^a  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Epidemic model; Global stability; Nonlinear birth; The reproduction number; Vector host

Indexed keywords

DISEASE CONTROL; DYNAMICS; OPEN CHANNEL FLOW; POPULATION STATISTICS; SYSTEM STABILITY; THEOREM PROVING;

BASIC REPRODUCTION NUMBERS; BIRTH RATES; CARRYING CAPACITIES; DEATH RATES; DEMOGRAPHIC PARAMETERS; DYNAMICAL BEHAVIORS; ENDEMIC EQUILIBRIUMS; EPIDEMIC MODEL; EPIDEMIC MODELS; GLOBAL STABILITIES; GLOBAL STABILITY; NONLINEAR BIRTH; SUFFICIENT CONDITIONS; THE REPRODUCTION NUMBER; THRESHOLD CONDITIONS; VARIABLE POPULATIONS; WEST NILE VIRUSES;

VECTORS;

EID: 55649117307     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.09.002     Document Type: Article

References (27)

1. 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
2. Wang W.D., and Ma Z. Global dynamics of an epidemic model with time delay. Nonlinear Anal. RWA 3 (2002) 365-373
3. Wang W.D., and Zhao X.Q. An epidemic model in a patchy environment. Math. Biosci. 190 (2004) 97-112
4. Feng Z.L., and Velasco-Hernández J.X. Competitive exclusion in a vector-host model for the dengue fever. J. Math. Biol. 35 (1997) 523-544
5. Cruz-Pachecoa G., Estevab L., Montano-Hirosec J.A., and Vargasd C. Modelling the dynamics of West Nile Virus. Bull. Math. Biol. 67 (2005) 1157-1172
6. Bowman C., Gumel A.B., Wu J., van den Driessche P., and Zhu H. A mathematical model for assessing control strategies against West Nile virus. Bull. Math. Biol. 67 (2005) 1107-1133
7. J.F. Jiang, Z.P. Qiu, J. Wu, H. Zhu, Threshold conditions for West Nile virus outbreaks, Bull. Math. Biol. (submitted for publication)
8. J.F. Jiang, Z.P. Qiu, The complete classification for dynamics in a nine dimensional West Nile virus model, SIAM J Appl. Math. (submitted for publication)
9. Tumwiine J., Mugisha J.Y.T., and Luboobi L.S. A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity. Appl. Math. Comput. 189 (2007) 1953-1965
10. Wei H.-M., Li X.-Z., and Martcheva M. An epidemic model of a vector-borne disease with direct transmission and time delay. J. Math. Anal. Appl. (2008) 10.1016/j.jmaa.2007.12.058
11. Anderson R.M., and May R.M. Co-evolution of host and parasites. Parasitology 85 (1982) 411-426
12. Brauer F. Models for the spread of universally fatal diseases. J. Math. Biol. 28 (1990) 451-462
13. Bremermann H.J., and Thieme H.R. A competitive exclusion principle for pathogen virulence. J. Math. Biol. 27 (1989) 179-190
14. Pugliese A. Population models for diseases with no recovery. J. Math. Biol. 28 (1990) 65-82
15. Gao L.Q., and Hethcote H.W. Disease transmission models with density-dependent demographics. J. Math. Biol. 30 (1992) 717-731
16. Cooke K., van den Driessche P., and Zou X. Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39 (1999) 332-352
17. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599-653
18. 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
19. Jiang J.F. On the global stability of cooperative systems. Bull. London Math. Soc. 6 (1994) 455-458
20. Thieme H.R. Persistence under relaxed point-dissipativity with an application to an epidemic model. SIAM J. Math. Anal. 24 (1993) 407-435
21. Smith H.L. Monotone dynamical systems: An introduction to theory of competitive and cooperative systems. Math. Surveys Monogr. vol. 41 (1995), AMS, Providence, RI
22. Castillo-Chavez C., and Thieme H.R. Asymptotically autonomous epidemic models. In: Arino O., and Kimmel M. (Eds). Mathematical Population Dynamics: Analysis of Heterogeneity. Theory of Epidemics. Wuetz 1 (1995) 33-50
23. Smith R.A. Some applications of Hausdorff dimension inequalities for ordinary differential equations. Proc. Roy. Soc. Edinburgh Sect. A 104 (1986) 235-259
24. Li M.Y., and Muldowney J. On Bendixson's criterion. J. Differential Equations 106 (1994) 27-39
25. Li M.Y., and Muldowney J. A geometric approach to global-stability problems. SIAM J. Math. Anal. 27 (1996) 1070-1083
26. Martin Jr. R.H. Logarithmic norms and projections applied to linear differential systems. J. Math. Anal. Appl. 45 (1974) 432-454
27. Muldowney J.S. Dichotomies and asymptotic behavior for linear differential systems. Trans. Amer. Math. Soc. 283 (1984) 465-484