A class of delayed HIV-1 infection models with latently infected cells was proposed. The basic reproductive number R0 was defined, and the existence conditions of disease-free equilibrium P0(x0, 0, 0, 0) and chronic-infection equilibrium P*(x*, ω*, y*, v*) were given. First, the local asymptotic stability of infection-free equilibrium and chronicinfection equilibrium was obtained by the linearization method. Further, by constructing the corresponding Lyapunov functions and using LaSalle's invariant principle, it was proved that when the basic reproductive number R0 was less than or equal to unity, the infection-free equilibrium P0(x0, 0, 0, 0) was globally asymptotically stable; moreover, when the basic reproductive number R0 was greater than unity, the chronic-infective equilibrium P*(x*, ω*, y*, v*) was globally asymptotically stable, but the infection-free equilibrium P0(x0, 0, 0, 0) was unstable. The results showed that a latently infected delay and an intracellular delay did not affect the global stability of the model, and numerical simulations were carried out to illustrate the theoretical results.
YANG Jun-xian
,
XIE Bao-ying
. A class of delayed HIV-1 infection models with latently infected cells[J]. Journal of East China Normal University(Natural Science), 2019
, 2019(4)
: 19
-32
.
DOI: 10.3969/j.issn.1000-5641.2019.04.003
[1] 孙起麟. 艾滋病病毒感染和治疗动力学的理论研究与应用[D]. 北京:北京科技大学, 2015.
[2] 王开发, 邱志鹏, 邓国宏. 病毒感染群体动力学模型分析[J]. 系统科学与数学, 2003, 32(4):433-443.
[3] PERELSON A S, NELSON P W. Mathematical models of HIV dynamics in vivo[J]. SIAM Review, 1999, 41(1):3-44
[4] NOWAK M A, ANDERSON R M, BOERLIJST M C, et al. HIV-1 evolution and disease progression[J], Science, 1996, 274(5289):1008-1011.
[5] KOROBEINIKOV A. Global properties of basic virus dynamics models[J]. Bulletin of Mathematical Biology, 2004, 66(4):879-883.
[6] NOWAK M A, BANGHAM C R M. Population dynamics of immune responses to persistent viruses[J]. Science, 1996, 272(5258):74-79.
[7] SONG X Y, NEUMANN A U. Global stability and periodic solution of the viral dynamics[J]. Journal of Mathematical Analysis and Applications, 2007, 329(1):281-297.
[8] BEDDINGTON J R. Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency[J]. Journal of Animal Ecology, 1975, 44(1):331-340.
[9] DEANGELIS D L, GOLDSTEIN R A, O'NEILL R V. A model for tropic interaction[J]. Ecology, 1975, 56(4):881-892.
[10] XU R. Global stability of an HIV-1 infection model with saturation infection and intracellular delay[J]. Journal of Mathematical Analysis and Application, 2011, 375(1):75-81.
[11] GUO T, LIU H H, XU C L, et al. Dynamics of a delayed HIV-1 infection model with saturation incidence rate and CTL immune response[J]. International Journal of Bifurcation and Chaos, 2016, 26(4):1-26.
[12] BAGASRA O, POMERANTZ R J. Human immunodeficiency virus type-I provirus is demonstrated in peripheral blood monocytes in vivo:A study utilizing an in situ polymerase chain reaction[J]. AIDS Research and Human Retroviruses, 1993, 9(1):69-76.
[13] PACE M J, AGOSTO L, GRAF E H. HIV reservoirs and latency models[J]. Virology, 2011, 411(2):344-354.
[14] CAPISTRÁN M A. A study of latency, reactivation and apoptosis throughout HIV pathogenesis[J]. Mathematical and Computer Modelling, 2010, 52(7/8):1011-1015.
[15] WANG H B, XU R, WANG Z W, et al. Global dynamics of a class of HIV-1 infection models with latently infected cells[J]. Nonlinear Analysis:Modeling and Control, 2015, 20(1):21-37.
[16] HALE J K, LUNEL S V. Introduction to Functional Differential Equations[M]. New York:Springer, 1993.