Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (4): 19-32.doi: 10.3969/j.issn.1000-5641.2019.04.003

• Mathematics • Previous Articles     Next Articles

A class of delayed HIV-1 infection models with latently infected cells

YANG Jun-xian, XIE Bao-ying   

  1. School of Science, Anhui Agricultural University, Hefei 230036, China
  • Received:2018-05-16 Online:2019-07-25 Published:2019-07-18

Abstract: 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.

Key words: HIV-1 infection model, latently infected cells, delay, Lyapunov function

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