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Impact of delays in cell infection and virus production on HIV-1 dynamics. (English) Zbl 1155.92031
Summary: Analysed is a mathematical model for HIV-1 infection with two delays accounting, respectively, for (i) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and (ii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproduction number $\cal R_0$ is identified and its threshold property is discussed: the uninfected steady state is proved to be globally asymptotically stable if $\cal R_0 < 1$ and unstable if $\cal R_0 > 1$. In the latter case, an infected steady state occurs and is proved to be locally asymptotically stable. The formula for $\cal R_0$ shows that increasing either of the two delays will decrease $\cal R_0$. This may suggest a new direction for new drugs-drugs that can prolong the latent period and/or slow down the virus production process.

92C60Medical epidemiology
34K20Stability theory of functional-differential equations
34D23Global stability of ODE
65C20Models (numerical methods)
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