Abstract
ABSTRACTIn this paper, a within-host HIV-1 infection model with virus-to-cell and direct cell-to-cell transmission and explicit age-since-infection structure for infected cells is investigated. It is shown that the model demonstrates a global threshold dynamics, fully described by the basic reproduction number. By analysing the corresponding characteristic equations, the local stability of an infection-free steady state and a chronic-infection steady state of the model is established. By using the persistence theory in infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is shown that if the basic reproduction number is less than unity, the infection-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the chronic-infection steady state is globally asymptotically stable. Numerical simulations are carried out to illustrate the feasibility of the theoretical results.
Highlights
In past decades, great attention has been paid to the within-host dynamics of HIV using mathematical modelling
By using the persistence theory in infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity
By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is shown that if the basic reproduction number is less than unity, the infection-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the chronic-infection steady state is globally asymptotically stable
Summary
Great attention has been paid to the within-host dynamics of HIV using mathematical modelling. Motivated by the works of Lai and Zou [11], Nelson et al [15] and Regoes et al [22], in the present paper, we are concerned with the joint effects of age since infection, direct cell-to-cell transfer and virus-to-cell infection on the dynamics of HIV-1 infection. To this end, we consider the following within-host HIV-1 infection model:. A brief discussion is given in Section 8 to conclude this work
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