Mathematical analysis of delay differential equation models of HIV-1 infection

Stability analysis of within-host parasite models with delays

“…the disappearance of the parasite when entering the target cell is neglected) and ϕ(x) = Λ − µ x x, this condition is automatically satisfied, hence R 0 > 1 is a necessary and sufficient (NSC) for the GAS of the infected equilibrium. In Section 6 we apply the preceding results to models studied by Nelson and Perelson in [15]. We come across the results of these authors and improve some of them.…”

“…This is the case of numerous models of the literature. See for example the general model (1) of [15] or the model in [21].…”

“…A widely used family of functions is given by the family of gamma distributions. Using a continuous distributed lag with a general kernel function g the following model has been proposed in [15]. In this model (2) it is assumed that the infected cell start to produce parasites τ time units after initial infection.…”

“…The value of τ varies according to a probability density function g. The term e −mτ accounts for cells infected at time t but that die before producing parasites. In [14,15] the function g is chosen as a gamma distribution. More complex functions can also be used.…”

“…This is not only for the sake of generality but we will need this refinement in our applications. For instance the application of the linear chain trick to the HIV-model of [15] gives a system for which the coefficients are different.…”