Citation: |
[1] |
R. M. Anderson, G. F. Medley, R. M. May and A. M. Johnson, A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS, IMA J. Math. Med. Biol., 3 (1986), 229-263. |
[2] |
R. M. Anderson and R. M. May, "Infectious Diseases in Humans: Dynamics and Control," Oxford University Press, Oxford, 1991. |
[3] |
E. A. Barbashin, "Introduction to the Theory of Stability," Wolters-Noordhoff, Groningen, 1970. |
[4] |
E. Beretta and V. Capasso, On the general structure of epidemic systems. Global asymptotic stability, Computers & Mathematics with Applications, 12-A (1986), 677-694. |
[5] |
E. Beretta and V. Capasso, Global stability results for a multigroup SIR epidemic model, in "Mathematical Ecology" (eds. T. G. Hallam, L. J. Gross and S. A. Levin), World Scientific Publ., Teaneck, NJ, (1988), 317-342. |
[6] |
O. Diekmann, J. A. P. Heesterbek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. |
[7] |
Z. Feng and H. R. Thieme, Endemic model with arbitrarily distributed periods of infection I. Fundamental properties of the model, SIAM J. Appl. Math. 61 (2000), 803-833. |
[8] |
P. Georgescu and Y.-H. Hsieh, Global stability for a virus dynamics model with nonlinear incidence of infection and removal, SIAM J. Appl. Math., 67 (2006/07), 337-353. |
[9] |
B.-S. Goh, "Management and Analysis of Biological Populations," Elsevier Science, Amsterdam, 1980. |
[10] |
A. B. Gumel, C. C. McCluskey and P. van den Driessche, Mathematical study of a staged-progression HIV model with imperfect vaccine, Bull. Math. Biol., 68 (2006), 2105-2128. |
[11] |
H. Guo and M. Y. Li, Global dynamics of a staged progression model for infectious diseases, Math. Biosci. Eng., 3 (2006), 513-525. |
[12] |
H. Guo and M. Y. Li, Global dynamics of a staged-progression model with amelioration for infectious diseases, J. Biol. Dynamics, 2 (2008), 154-168. |
[13] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653. |
[14] |
H. W. Hethcote, J. W. VanArk and I. M. Longini Jr., A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation, Math. Biosci., 106 (1991), 203-222. |
[15] |
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. |
[16] |
J. M. Hyman, J. Li and E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci., 155 (1999), 77-109. |
[17] |
W. O. Kermack and A. G. McKendrick, A Contribution to the mathematical theory of epidemics, Proc. Roy. Soc. Lond. A, 115 (1927), 700-721. |
[18] |
A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. Biol., 21 (2004), 75-83. |
[19] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883. |
[20] |
A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68 (2006), 615-626. |
[21] |
A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886. |
[22] |
A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate, Math. Med. Biol., 26 (2009), 225-239. |
[23] |
A. Korobeinikov, Stability of ecosystem: Global properties of a general prey-predator model, Math. Med. Biol., 26 (2009), 309-321. |
[24] |
A. Korobeinikov, Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages, Bull. Math. Biol., 71 (2009), 75-83.doi: 10.1007/s11538-007-9196-y. |
[25] |
J. P. LaSalle, "The Stability of Dynamical Systems," SIAM, Philadelphia, 1976. |
[26] |
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. |
[27] |
A. M. Lyapunov, "The General Problem of the Stability of Motion," Taylor & Francis, Ltd., London, 1992. |
[28] |
W. Ma, M. Song and Y. Takeuchi, Global stability for an SIR epidemic model with time delay, Appl. Math. Lett., 17 (2004), 1141-1145. |
[29] |
C. C. McCluskey, A model of HIV/AIDS with staged progression and amelioration, Math. Biosci., 181 (2003), 1-16. |
[30] |
C. C. McCluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Math. Biosci. Eng., 3 (2006), 603-614. |
[31] |
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. |
[32] |
C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), 603-610. |
[33] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay - distributed or discrete, Nonlinear Anal. - Real, 11 (2010), 55-59. |
[34] |
C. C. McCluskey, P. Magal and G. F. Webb, Liapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140. |
[35] |
D. Morgan, C. Mahe, B. Mayanja, J. M. Okongo, R. Lubega and J. A. Whitworth, HIV-1 infection in rural Africa: Is there a difference in median time to AIDS and survival compared with that in industrialized countries, AIDS, 16 (2002), 597-632. |
[36] |
D. Okuonghae and A. Korobeinikov, Dynamics of tuberculosis: The effect of direct observation therapy strategy (DOTS) in Nigeria, Math. Model. Nat. Phenom., 2 (2006), 99-111. |
[37] |
G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402. |
[38] |
Y. Takeuchi, "Global Dynamical Properties of Lotka-Volterra Systems," World Scientific, Singapore, 1996. |
[39] |
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. |
[40] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two infinite delays, Math. Med. Biol., 2011. (doi:10.1093/imammb/dqr009) |