Stability of a stochastic model for HIV-1 dynamics within a host

References

• Korobeinikov A. Lyapunov functions and global properties for SEIR and SEIS epidemic models. Math. Med. Biol. 2004;21:75–83.
   PubMed Web of Science ®Google Scholar
• Korobeinikov A. Global properties of basic virus dynamics models. Bull. Math. Biol. 2004;66:879–883.
   PubMed Web of Science ®Google Scholar
• Adda P, Dimi JL, Iggidr A, Kamgang JC, Sallet G, Tewa JJ. General models of host-parasite systems. Global analysis. Disc. Cont. Dyn. Syst. B. 2007;8:1–17.
   Web of Science ®Google Scholar
• Fall A, Iggidr A, Sallet G, Tewa JJ. Epidemiological models and Lyapunov functions. Math. Model. Nat. Phenom. 2007;2:62–83.
   Web of Science ®Google Scholar
• Korobeinikov A. Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages. Bull. Math. Biol. 2009;71:75–83.
   PubMed Web of Science ®Google Scholar
• Melnik AV, Korobeinikov A. Global asymptotic properties of staged models with multiple progression pathways for infectious diseases. Math. Biosci. Eng. 2011;8:1019–1034.
   PubMed Web of Science ®Google Scholar
• Okuonghae D, Korobeinikov A. Dynamics of tuberculosis: the effect of direct observation therapy strategy (DOTS) in Nigeria. Math. Model. Nat. Phenom. 2006;2:99–111.
   Google Scholar
• Korobeinikov A. Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission. Bull. Math. Biol. 2006;68:615–626.
   PubMed Web of Science ®Google Scholar
• Korobeinikov A. Global properties of infectious disease models with non-linear incidence. Bull. Math. Biol. 2007;69:1871–1886.
   PubMed Web of Science ®Google Scholar
• Korobeinikov A. Stability of ecosystem: global properties of a general prey-predator model. Math. Med. Biol. 2009;26:309–321.
   PubMed Web of Science ®Google Scholar
• Korobeinikov A. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Disc. Cont. Dyn. Syst. Ser. B. 2010;14:1095–1103.
   Web of Science ®Google Scholar
• McCluskey CC. Global stability for a class of mass action systems allowing for latency in tuberculosis. Math. Anal. Appl. 2008;338:518–535.
   Web of Science ®Google Scholar
• McCluskey CC. Complete global stability for an SIR epidemic model with delay – distributed or discrete. Nonlinear Anal. B. 2010;11:55–59.
   Web of Science ®Google Scholar
• McCluskey CC. Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. Math. Biosci. Eng. 2009;6:603–610.
   PubMed Web of Science ®Google Scholar
• Magal P, McCluskey CC, Webb GF. Liapunov functional and global asymptotic stability for an infection-age model. Appl. Anal. 2010;89:1109–1140.
   Web of Science ®Google Scholar
• Melnik AV, Korobeinikov A. Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Math. Biosci. Eng. 2013;10:369–378.
   PubMed Web of Science ®Google Scholar
• Nowak MA, May RM. Virus dynamics: mathematical principles of immunology and virology. New York (NY): Oxford University Press; 2000.
   Google Scholar
• Shaikhet L. Lyapunov functionals and stability of stochastic functional differential equations. London: Springer; 2013.
   Google Scholar
• Korobeinikov A. Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate. Math. Med. Biol. 2009;26:225–239.
   PubMed Web of Science ®Google Scholar
• Beretta E, Kolmanovskii V, Shaikhet L. Stability of epidemic model with time delays influenced by stochastic perturbations. Math. Comput. Simul. 1998;45:269–277. Special Issue “Delay Systems”.
   Web of Science ®Google Scholar
• Shaikhet L. Lyapunov functionals and stability of stochastic difference equations. London: Springer; 2011.
   Google Scholar
• Caraballo T, Real J, Shaikhet L. Method of Lyapunov functionals construction in stability of delay evolution equations. J. Math. Anal. Appl. 2007;334:1130–1145.
   Web of Science ®Google Scholar
• Gantmacher FR. The theory of matrices. Vol. 2. New York (NY): Chelsea Pub. Co.; 1959.
   Google Scholar
• Gikhman II, Skorokhod AV. Stochastic differential equations. Berlin: Springer; 1972.
   Google Scholar