A model of HIV-1 pathogenesis that includes an intracellular delay

Stability analysis of within-host parasite models with delays

“…The omega limit set of this trajectory is included inẆ = 0. ButẆ = 0 is reduced to {(x * , 0, 0)} since C(−A −1 )B > 0 and ϕ satisfies the hypothesis (13). This ends the proof of the global stability of the PFE.…”

“…The number of infectious virus released N is not known precisely, but values over 10 3 are possible. If we choose N = 480 (see [13]) we get R 0 = 2.74 and if we choose (1 − n rt )(1 − n p ) = 0.5 we obtain, with treatment, R 0 = 1.37. A destabilizinḡ τ should satisfy mτ > 0.316.…”

“…The foregoing analysis makes no allowance for the biologically sensible values of the parameters. For example using the parameters of the references [2,38,3,13] we set s = 10 (reference [13]) , d T = 0.02 (reference [2]), k = 3.43 10 −5 (see [13]) , c = 3 (see [13,3]). With these values we obtain for R 0 without treatment R 0 = 0.0057 N .…”

“…This is not biologically sensible. Therefore models with delays have been considered [12,13] . Two kinds of delays are encountered in the literature, namely discrete constant delays and continuously distributed delays.…”

A viral load-based cellular automata approach to modeling HIV dynamics and drug treatment

“…The basic class of ODE HIV models (Culshaw and Ruan, 2000;Nelson and Perelson, 2002;Nelson et al, 2000;Perelson and Nelson, 1999) generally includes variables that represent the healthy cells T, infected cells T Ã , and the viral load V. The viral load is an integral part of the system of equations that influences the dynamics of the healthy and infected cells.…”