Mathematical Biosciences and Engineering (MBE)

Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes
Pages: 819 - 841, Issue 4, October 2012

doi:10.3934/mbe.2012.9.819      Abstract        References        Full text (459.2K)           Related Articles

C. Connell McCluskey - Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada (email)

1 S. M. Blower, A. R. McLean, T. C. Porco, P. M. Small, P. C. Hopwell, M. A. Sanchez and A. R. Moss, The intrinsic transmission dynamics of tuberculosis epidemics, Nature Medicine, 1 (1995), 815-821.
2 E. M. C. D'Agata, P. Magal, D. Olivier, S. Ruan and G. F. Webb, Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration, J. Theoret. Biol., 249 (2007), 487-499.
3 O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $\mathcal R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.       
4 Z. Feng and H. Thieme, Endemic models with arbitrarily distributed periods of infection I: fundamental properties of the model, SIAM J. Appl. Math., 61 (2000), 803-833.       
5 H. Guo and M. Y. Li, Global dynamics of a staged progression model with amelioration for infectious diseases, J. of Biol. Dyn., 2 (2008), 154-168.       
6 J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Amer. Math. Soc., Providence, 1988.       
7 H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.       
8 F. Hoppensteadt, An age dependent epidemic problem, J. Franklin Inst., 297 (1974), 325-333.
9 J. Hyman, J. Li and E. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci., 155 (1999), 77-109.
10 A. Iggidr, J. Mbang, G. Sallet and J.-J. Tewa, Multi-compartment models, Discrete Contin. Dyn. Syst. Ser. Supplement, (2007), 506-519.       
11 W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. London, Ser. A, 115 (1927), 700-721.
12 A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. and Biol., 21 (2004), 75-83.       
13 M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 (1995), 155-164.       
14 X. Lin, H. W. Hethcote and P. van den Driessche, An epidemiological model for HIV/AIDS with proportional recruitment, Math. Biosci., 118 (1993), 181-195.       
15 P. Magal, C. C. McCluskey and G. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Applicable Analysis, 89 (2010), 1109-1140.       
16 C. C. McCluskey, A model of HIV/AIDS with staged progression and amelioration, Math. Biosci., 181 (2003), 1-16.       
17 C. C. McCluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Math. Biosci. and Eng., 3 (2006), 603-614.       
18 C. C. McCluskey, Global stability for a class of mass action systems allowing for latency in tuberculosis, J. Math. Anal. Appl., 338 (2008), 518-535.       
19 C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. and Eng., 6 (2009), 603-610.       
20 C. C. McCluskey, Complete global stability for an SIR epidemic model with delay - distributed or discrete, Nonlinear Anal. RWA, 11 (2010), 55-59.       
21 C. C. McCluskey, Global stability for an SIR epidemic model with delay and general nonlinear incidence, Math. Biosci. and Eng., 7 (2010), 837-850.       
22 C. C. McCluskey, Global stability for an SIR epidemic model with delay and nonlinear incidence, Nonlinear Anal. RWA, 11 (2010), 3106-3109.       
23 G. Röst, SEI model with varying transmission and mortality rates, in "Mathematic in Science and Technology: Mathematical Methods, Models and Algorithms in Science and Technology, Proceedings of the Satellite Conference of ICM 2010" (eds. A. H. Siddiqi, R. C. Singh and P. Manchanda), World Scientific, (2011) 489-498.       
24 G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. and Eng., 5 (2008), 389-402.       
25 H. L. Smith and H. R. Thieme, "Dynamical Systems and Population Persistence," Amer. Math. Soc., Providence, 2011.       
26 H. R. Thieme and C. Castillo-Chavez, How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?, SIAM J. Appl. Math., 53 (1993), 1447-1479.       
27 G. F. Webb, "Theory of Nonlinear Age-Dependent Population Dynamics," Marcel Dekker, New York, 1985.       

Go to top