Mathematical Biosciences and Engineering (MBE)

Global stability for epidemic model with constant latency and infectious periods
Pages: 297 - 312, Issue 2, April 2012

doi:10.3934/mbe.2012.9.297      Abstract        References        Full text (365.3K)           Related Articles

Gang Huang - School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China (email)
Edoardo Beretta - CIMAB, University of Milano, via C. Saldini 50, I20133 Milano, Italy (email)
Yasuhiro Takeuchi - Graduate School of Science and Technology, Shizuoka University, Hamamatsu, 4328561, Japan (email)

1 J. Arino and P. van den Driessche, Time delays in epidemic models: Modeling and numerical considerations, in "Delay Differential Equations and Applications" (eds. O. Arino, M. L. Hbid and E. Ait Dads), Springer, (2006), 539-578.
2 E. Beretta and D. Breda, An SEIR epidemic model with constant latency time and infectious period, Math. Biosci. Eng., 8 (2011), 931-952.
3 E. Beretta and Y. Takeuchi, Global stability of an SIR model with time delays, J. Math. Biol., 33 (1995), 250-260.       
4 E. Beretta, T. Hara, W. Ma and Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay, Nonlinear Anal., 47 (2001), 4107-4115.       
5 J. M. Cushing, "An Introduction to Structured Population Dynamics," CBMS-NSF Regional Conference Series in Applied Mathematics, 71, SIAM, 1998.
6 Y. Enatsu, Y. Nakata and Y. Muroya, Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays, Discrete and Continuous Dynamical Systems Ser. B, 15 (2011), 61-74.       
7 G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207.       
8 G. Huang and Y. Takeuchi, Global analysis on delay epidemiological dynamic models with nonlinear incidence, J. Math. Biol., 63 (2011), 125-139.       
9 G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.
10 A. Korobeinikov and P. K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng., 1 (2004), 57-60.       
11 A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68 (2006), 615-626.       
12 A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1889.       
13 M. Iannelli, "Mathematical Theory of Age-Structured Population Dynamics," Applied Mathematical Monographs, 7, Consiglio Nazionale delle Ricerche, CNR, Giardini Editori e Stampatori in Pisa, Aprile, 1995.
14 A. V. Melnik and A. Korobeinikov, Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility, (2011), preprint.
15 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.       
16 C. C. McCluskey, Delay versus age-of-infection-global stability, Appl. Math. Comput., 217 (2010), 3046-3049.       
17 C. C. McCluskey, Global stability for an SIR epidemic model with delay and nonlinear incidence, Nonlinear Anal. RWA, 11 (2010), 3106-3109.       
18 C. C. McCluskey, Global stability of an SIR epidemic model with delay and general nonlinear incidence, Math. Biosci. Eng., 7 (2010), 837-850.       
19 P. van den Driessche, Some epidemiological models with delays, in "Differential Equations and Applications to Biology and To Industry" (eds. M. Martell, K. Cooke, E. Cumberbatch, R. Tang and H. Thieme), World Scientific, (1994), 507-520.
20 G. F. Webb, "Theory of Nonlinear Age-Dependent Population Dynamics," Marcel Dekker, New York, 1985.
21 R. Xu and Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. RWA, 10 (2009), 3175-3189.       
22 R. Xu and Y. Du, A delayed SIR epidemic model with saturation incidence and a constant infectious period, J. Appl. Math. Comput., 35 (2011), 229-250.       

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