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

作者: Leonid Shaikhet , Andrei Korobeinikov

DOI: 10.1080/00036811.2015.1058363

关键词: Statistical physicsThermodynamic equilibriumLyapunov exponentMathematicsControl theoryLyapunov equationStochastic modellingStability (probability)Lyapunov functionDynamics (mechanics)Host (network)

摘要: We consider a stochastically perturbed Nowak–May model of virus dynamics within host. Using the direct Lyapunov method, we found sufficient conditions for stability in probability equilibrium states this model.

参考文章(25)
Iosif Il’ich Gihman, Anatolii Vladimirovich Skorohod, Stochastic Differential Equations ,(1972)
A. Fall, A. Iggidr, G. Sallet, J. J. Tewa, Epidemiological Models and Lyapunov Functions Mathematical Modelling of Natural Phenomena. ,vol. 2, pp. 62- 83 ,(2007) , 10.1051/MMNP:2008011
C. Connell McCluskey, Complete global stability for an SIR epidemic model with delay — Distributed or discrete Nonlinear Analysis-real World Applications. ,vol. 11, pp. 55- 59 ,(2010) , 10.1016/J.NONRWA.2008.10.014
P. Magal, C.C. McCluskey, G.F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model Applicable Analysis. ,vol. 89, pp. 1109- 1140 ,(2010) , 10.1080/00036810903208122
Andrei Korobeinikov, Global Properties of Infectious Disease Models with Nonlinear Incidence Bulletin of Mathematical Biology. ,vol. 69, pp. 1871- 1886 ,(2007) , 10.1007/S11538-007-9196-Y
Andrei Korobeinikov, , Global properties of a general predator-prey model with non-symmetric attack and consumption rate Discrete and Continuous Dynamical Systems-series B. ,vol. 14, pp. 1095- 1103 ,(2010) , 10.3934/DCDSB.2010.14.1095
T. Caraballo, J. Real, L. Shaikhet, Method of Lyapunov functionals construction in stability of delay evolution equations Journal of Mathematical Analysis and Applications. ,vol. 334, pp. 1130- 1145 ,(2007) , 10.1016/J.JMAA.2007.01.038