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Mathematical Biosciences and Engineering (MBE)
 

Global stability of an age-structured cholera model
Pages: 641 - 665, Issue 3, June 2014

doi:10.3934/mbe.2014.11.641      Abstract        References        Full text (469.5K)           Related Articles

Jianxin Yang - Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China (email)
Zhipeng Qiu - Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China (email)
Xue-Zhi Li - Department of Mathematics, Xinyang Normal University, Xinyang 464000, China (email)

1 J. R. Andrews and S. Basu, Transmission dynamics and control of cholera in Haiti: An epidemic model, Lancet, 377 (2011), 1248-1255.
2 O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infections diseases in hetereogeneous populations, J. Math. Biol., 28 (1998), 365-382.       
3 O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infections Disease: Model Building, Analysis and Interpretation, Wiley, New York, 2000.       
4 Z. L. Feng, W. Z. Huang and C. Castillo-Chavez, Global behavior of a multi-group SIS epidemic model with age structure, J. Diff. Equs., 218 (2005), 292-324.       
5 H. I. Freedman and J. W. H. So, Global stability and persistence of simple food chains, Math. Biosci., 76 (1985), 69-86.       
6 B. S. Goh, Global stability in many-species systems, Amer. Natur., 111 (1977), 135-143.
7 J. K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs 25, American Mathematical Society, Providence, RI, 1988.       
8 J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.       
9 J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection, Cambridge University Press, Cambridge, 1988.       
10 G. Huang, X. N. Liu and Y. Takeuchi, Lyapunov function and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.       
11 M. Iannelli, Mathematical Theory of Age-structured Population Dynamics, Applied Mathematics Monographs 7, comitato nazionale per le scienze matematiche, Consiglio Nazionale delle Ricerche (C. N. R), Giardini, Pisa, 1995.
12 H. Inaba, A semigroup approach to the strong ergodic theorem of the multistate stable population process, Math. Popul. Studi., 17 (1988), 47-77.       
13 A. L. Lloyd, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods, Proc. Roy. Soc. Lond. B, 268 (2001), 985-993.
14 A. L. Lloyd, Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics, Theor. Popul. Biol., 60 (2001), 59-71.
15 P. Magal, Compact attractors for time periodic age-structured population models, Electron. J. Diff. Equs., 65 (2001), 1-35.       
16 P. Magal and H. R. Thieme, Eventual compactness for a semiflow generated by an age-structured models, Communications on Pure and Applied Analysis, 3 (2004), 695-727.       
17 P. Magal and X. Q. Zhao, Global attracotor in uniformly persistence dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.       
18 E. D'Agata, P. Magal, S. Ruan and G. F. Webb, Asymptotical behavior in nosocomial epidemic model with antibiotic resistance, Diff. Integr. Equs., 19 (2006), 573-600.       
19 P. Magal, C. C. McCluskey and G. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.       
20 P. Magal and C. McCluskey, Two group infection age model: an application to nosocomial infection, SIAM J. Appl. Math., 73 (2013), 1058-1095.       
21 F. A. Milner and A. Pugliese, Periodic solutions: a robust numerical method for an SIR model of epidemics, J. Math. Biol., 39 (1999), 471-492.       
22 Z. S. Shuai and P. Van den Driessche, Global dynamics of cholera models with differential infectivity, Math. Biosci., 234 (2011), 118-126.       
23 Z. S. Shuai, J. H. Tien and P. van den Driessche, Cholera models with hyperinfectivity and temporary immunity, Bull. Math. Biol., 74 (2010), 2423-2445.       
24 H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Diff. Integr. Equs., 3 (1990), 1035-1066.       
25 H. R. Thieme and C. Castillo-Chavez, How may infection-age-dependent infectivity affect the dynamics if HIV/AIDs? SIAM J. Appl. Math., 53 (1993), 1447-1479.       
26 J. P. Tian, S. Liao and J. Wang, Dynamical Analysis and Control Strategies in Modeling Cholera, 2010. Available from: http://www.math.wm.edu/~jptian/preprints/pr-7-ode-cholera.pdf.
27 J. P. Tian and J. Wang, Global stability for cholera epidemic model, Math. Biosci., 232 (2011), 31-41.       
28 J. H. Tien and D. J. D. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bull. Math. Biol., 72 (2010), 1506-1533.       
29 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.       
30 G. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York, 1985.       

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