Global dynamic behavior of a multigroup cholera model with indirect transmission

Discrete Dynamics in Nature and Society

Volumn 2013, Issue , 2013, Pages

  Li, Ming Tao ^a   Sun, Gui Quan ^b,c,d   Zhang, Juan ^a   Jin, Zhen ^a,b  

^a NORTH UNIVERSITY OF CHINA   (China)

^b SHANXI UNIVERSITY   (China)

^c HANGZHOU NORMAL UNIVERSITY   (China)

^d FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84897585331     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2013/703826     Document Type: Article

References (32)

1. Jensen M. A., Faruque S. M., Mekalanos J. J., Levin B. R., Modeling the role of bacteriophage in the control of cholera outbreaks. Proceedings of the National Academy of Sciences of the United States of America 2006 103 12 4652 4657 2-s2.0-33645232900 10.1073/pnas.0600166103
2. Misra A. K., Singh V., A delay mathematical model for the spread and control of water borne diseases. Journal of Theoretical Biology 2012 301 49 56 10.1016/j.jtbi.2012.02.006 MR2902878
3. Torres Codeço C., Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infectious Diseases 2001 1, article 1 2-s2.0-2942619997 10.1186/1471-2334-1-1 (Pubitemid 38760847)
4. Pascual M., Bouma M. J., Dobson A. P., Cholera and climate: revisiting the quantitative evidence. Microbes and Infection 2002 4 2 237 245 2-s2.0-0036185525 10.1016/S1286-4579(01)01533-7 (Pubitemid 34183499)
5. Hartley D. M., Morris J. G. Jr., Smith D. L., Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics? PLoS Medicine 2006 3 1 63 69 2-s2.0-32044434020 10.1371/journal.pmed.0030007 (Pubitemid 43200633)
6. Mukandavire Z., Liao S., Wang J., Gaff H., Smith D. L., Morris J. G. Jr., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe. Proceedings of the National Academy of Sciences of the United States of America 2011 108 21 8767 8772 2-s2.0-79957773377 10.1073/pnas.1019712108
7. Mukandavire Z., Smith D. L., Morris J. G. Jr., Cholera in Haiti: reproductive numbers and vaccination coverage estimates. Scientific Reports 2013 3, article 997
8. Huang W. Z., Cooke K. L., Castillo-Chavez C., Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM Journal on Applied Mathematics 1992 52 3 835 854 10.1137/0152047 MR1163809 ZBL0769.92023
9. Feng Z., Velasco-Hernández J. X., Competitive exclusion in a vector-host model for the dengue fever. Journal of Mathematical Biology 1997 35 5 523 544 10.1007/s002850050064 MR1479326 ZBL0878.92025 (Pubitemid 127759099)
10. Bowman C., Gumel A. B., Van den Driessche P., Wu J., Zhu H., A mathematical model for assessing control strategies against West Nile virus. Bulletin of Mathematical Biology 2005 67 1107 1133 (Pubitemid 40912468)
11. Edwards R., Kim S., van den Driessche P., A multigroup model for a heterosexually transmitted disease. Mathematical Biosciences 2010 224 87 94
12. Lajmanovich A., York J. A., A deterministic model for gonorrhea in a nonhomogeneous population. Mathematical Biosciences 1976 28 221 236
13. Hethcote H. W., An immunization model for a heterogeneous population. Theoretical Population Biology 1978 14 3 338 349 2-s2.0-0018247773
14. Thieme H. R., Capasso V., Grosso E., Paveri-Fontana S. L., Local stability in epidemic models for heterogeneous populations. Mathematics in Biology and Medicine 1985 57 Springer 185 189 Lecture Notes in Biomathematics
15. Guo H., Li M. Y., Shuai Z., Global stability of the endemic equilibrium of multigroup SIR epidemic models. Canadian Applied Mathematics Quarterly 2006 14 259 284
16. Yuan Z., Wang L., Global stability of epidemiological models with group mixing and nonlinear incidence rates. Nonlinear Analysis. Real World Applications 2010 11 2 995 1004 2-s2.0-70449709108 10.1016/j.nonrwa.2009.01.040
17. Sun R., Shi J., Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. Applied Mathematics and Computation 2011 218 280 286
18. Li M. Y., Shuai Z., Wang C., Global stability of multi-group epidemic models with distributed delays. Journal of Mathematical Analysis and Applications 2010 361 38 47
19. Shu H., Fan D., Wei J., Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission. Nonlinear Analysis. Real World Applications 2012 13 4 1581 1592 2-s2.0-84856551488 10.1016/j.nonrwa.2011.11.016
20. Diekmann O., Heesterbeek J. A., Metz J. A., On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 1990 28 4 365 382 2-s2.0-0025159677
21. van den Driessche P., Watmough J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002 180 29 48 2-s2.0-0036845274 10.1016/S0025-5564(02) 00108-6 (Pubitemid 35304346)
22. Diekmann O., Heesterbeek J. A. P., Roberts M. G., The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface 2010 7 47 873 885 2-s2.0-77953160649 10.1098/rsif.2009.0386
23. Smith H. L., Waltman P., The Theory of the Chemostat 1995 Cambridge University Press
24. Thieme H.R., Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. Journal of Mathematical Biology 1992 30 755 763
25. Zhao X. Q., Jing Z. J., Global asymptotic behavior in some cooperative systems of functional differential equations. Canadian Applied Mathematics Quarterly 1996 4 421 444
26. Thieme H. R., Persistence under relaxed point-dissipativity (with application to an endemic model). Mathematical Biosciences 1993 166 407 435
27. Zhao X. Q., Uniform persistence and periodic coexistence states in infinitedimensional periodic semiflows with applications. Canadian Applied Mathematics Quarterly 1995 3 473 495
28. Wang W. D., Zhao X.-Q., An epidemic model in a patchy environment. Mathematical Biosciences 2004 190 1 97 112 2-s2.0-2542463400 10.1016/j.mbs.2002.11.001 (Pubitemid 38692826)
29. Guo H., Li M. Y., Shuai Z., A graph-theoretic approach to the method of global Lyapunov functions. Proceedings of the American Mathematical Society 2008 136 8 2793 2802 2-s2.0-70349388314 10.1090/S0002-9939-08-09341-6
30. Moon J. W., Counting Labelled Trees 1970 Montreal, Canada Canadian Mathematical Congress
31. Knuth D. E., The Art of Computer Programming 1997 1 Reading, Mass, USA Addison-Wesley
32. Lasalle J. P., The stability of dynamical systems. Proceedings of the Regional Conference Series in Applied Mathematics 1976 Philadelphia, Pa, USA SIAM