Table 1. Parameter definitions and values.

Parameter	Description	Value	Units	Reference
dT	Uninfected CD4+ T-cell death rate	0.01	per day	[18,53]
rT	CD4+ T-cell proliferation rate		per day	Estimated for individual macaques
κ	Carrying capacity for the CD4+ T cell population	a	cells/ml	Calculated
α	Latent cell activation rate	0.001	per day	[7]
dL	Latent cell death rate	b	per day	Calculated
rL	Latent cell proliferation rate	b	per day	Calculated
dL+ α -rL	Decay rate of the latent cell reservoir	0.0182b	per day	[32]
f	Fraction of infections resulting in latency	10−5		Calibratedc
m	Rate cytotoxic effector cells kill infected cell		ml/cell per day	Estimated for individual macaques
δ	Infected cell death rate due to viral cytopathic effects in baseline model	0.60	per day	Calibrated
p	Viral production rate		RNA copies per cell per day	Estimated for individual macaques
c	Viral clearance rate	23	per day	[54–56]
λE	Effector cell source rate	103	cells / ml per day	Calibratedd
μ	Death rate of cytotoxic effector cells	0.32	per day	[30]
bE	Maximum proliferation rate for cytotoxic effector cells	1.62	per day	[30,31]
dE	Maximum exhaustion rate for cytotoxic effector cells in baseline model	1.35	per day	Calibrated
KB	Saturation constant for cytotoxic effector cell expansion		cells/ml	Estimated for individual macaques
KD	Saturation constant for cytotoxic effector cell exhaustion	55 KB	cells/ml	[32]
ε	Efficacy of cART	0.90		Assumed
T(0)β	Free virus infection rate	5 ⨉ 10−3	cells/SIV RNA per day	Assumed
Aα4β7	Total amount of anti-α4β7 antibody infused	805	μg/ml	50 mg/kg for a 5.3 kg [57] macaque with 329 ml of blood
V(0)	Initial virus concentration	413	SIV RNA copies/ml	Estimated
k0	Elimination rate of anti-α4β7 antibody	0.048	per day	Estimated
k12	Distribution rate of anti-α4β7 antibody to tissue	0.165	per day	Estimated
k21	Distribution rate of anti-α4β7 antibody to blood from tissue	0.008	per day	Calibratede
κα4β7	Fraction of CD4+ T cells that are α4β7+	0.73		[1]
EC50	Half-maximal concentration for anti-α4β7 antibody binding to CD4 T cells	2.76 ⨉ 10-2	μg/ml	[58]
KP	Saturation constant for the source of effector cells in the saturated source model		cell/ml	Estimated for individual macaques
γ	Fold increase in viral clearance rate			Estimated for individual treated macaques
1/ψC	Antibody concentration of half-maximal effect for increased viral clearance		μg/ml	Estimated for individual treated macaques
1/ψN	Antibody concentration of half-maximal effect for neutralization	1/ψN = 1/ψC	μg/ml	Estimated for individual treated macaques
𝕀N	Indicator variable for the presence of the effect of viral neutralization from the anti-α4β7 antibody	1 when present; 0 otherwise
𝕀A	Indicator variable for the presence of the effect of an increase in the effector cell source rate from the anti-α4β7 antibody	1 when present; 0 otherwise
⍵	Maximum rate protection wanes		per day	Estimated for individual treated macaques
⍴	Maximum rate target cells become protected		per day	Estimated for individual treated macaques
Ω	Half-saturation constant for the effect the anti-α4β7 antibody has on increasing antigen presentation		μg/ml	Estimated for individual treated macaques

a The carrying capacity was calculated such that in the absence of productively infected and latently infected cells the CD4⁺ T cell population would be in steady state at the initial target cell concentration.

b Specifying the latent cell activation rate, the difference between the latent cell death rate and the latent cell proliferation rate is such that the half-life of the latent cell reservoir is 38 days.

c The fraction of infections resulting in latency was calibrated during the initial stages of fitting such that the viral load under cART was greater than 1 SIV RNA copies/ml during chronic HIV infection.

d The source rate of effector cells was chosen such that the effector cell concentration in the baseline model was relatively comparable to the concentration of HIV specific CD8⁺ T cells during HIV infection.

e The distribution rate of the antibody to the blood from the tissue was calibrated at 0.001 intervals to maximize the likelihood of the antibody dynamics from the pharmacokinetic model.