Figure 1

Models of the HIV infection.

(a) Schematic of the typical HIV model. The uninfected CD4⁺ T cells can self-renew (logistic growth), die at rate δ_T day⁻¹ and get infected at rate β particle⁻¹ day⁻¹. To model the influx from the naive compartment, uninfected T cells additionally get replenished at rate λ cells day⁻¹. Infected cells produce p virus particles cell⁻¹ day⁻¹ and die at rate δ_I day⁻¹. Viruses are cleared at rate c day⁻¹ (see section Models). (b) The infection rate in the typical HIV model (β) was reduced and is expressed as a percentage of the initial infection rate (β₀). Only once the infection rate is reduced below a certain threshold (β < β^*; vertical gray dashed line) will the viral load start to decrease. Several HIV-1 models let uninfected T cells be replenished at a constant rate from thymus, bone marrow, naive and memory T cells^13,14,23. A quantitavily similar model with a constant rate of replenishment (i.e. λ = 14.3 and r = 0 in Eq. 1) also has the property that β has to be decreased markedly (here more than 50%) to have a significant effect on the viral load¹⁴ (black dashed line). Modeling one μl of blood, the following parameter values were used: r = 0.06 day⁻¹, K = 1500 cells, δ_T = 0.02 day⁻¹, β₀ = 3.6 × 10⁻⁶ particle⁻¹ day⁻¹, δ_I = 1 day⁻¹, p = 2.14 × 10⁴ virus particles cell⁻¹ day⁻¹, c = 23 day⁻¹ (see section Models). The values of λ, r and K were chosen to have 1000 T cells per μl blood in the virus-free steady state. (c) For the GT model, we model two populations of uninfected T cells (normal and genetically modified) sharing logistic growth. Normal uninfected T cells additionally get replenished at rate λ cells day⁻¹. Normal and genetically modified T cells get infected at rate β_n and β_g particle⁻¹ day⁻¹ (where β_g ≤ β_n), respectively. Infected cells die at rate δ_n and δ_g day⁻¹.