Table 3 Model-2 (the best model) estimated parameters for individual animals, fitted parameter values to the group median data (the median data of each group), and their 95% confidence intervals in parentheses, and the mean values of εA calculated over a period of 200 days post infection using \(\overline{{\varepsilon }_{A}}=\frac{1}{200}{\int }_{0}^{200}(\frac{\eta A(t)}{1+\eta A(t)})dt\). For the rapid-progressor morphine group, we can obtain the analytic solution for \(\overline{{\varepsilon }_{A}}=\frac{\eta a}{1+\eta a}\).

From: Modeling the Effects of Morphine-Altered Virus Specific Antibody Responses on HIV/SIV Dynamics

Animal λ (cell ml−1day−1) r (day−1) q (day−1) δ (day−1) σ (ml ng−1day−1) η (ml ng−1) mean value \(\overline{{{\boldsymbol{\varepsilon }}}_{{\boldsymbol{A}}}}\)
Rapid-progressor morphine group
1/04L 3630 (3396–3901) 0.20 (0.14– 0.28) 1.1 × 10−4 (1.5 × 10−5–2.1 × 10−4) 0.56 (0.43–0.75) 2.8 × 10−3 (6.8 × 10−4–5.1 × 10−3) 1.0 × 10−4 (1.8 × 10−6–1.9 × 10−4) 5.0 × 10−5
1/28Q 3773 (3322–4481) 0.24 (0.18–0.48) 1.0 × 10−4 (2.6 × 10−5–1.4 × 10−4) 0.80 (0.68–0.94) 2.3 × 10−3 (8.0 × 10−5–3.0 × 10−3) 1.1 × 10−4 (1.9 × 10−8–1.2 × 10−4) 5.0 × 10−5
1/42N 5000 (4688–5278) 0.40 (0.16–0.69) 1.2 × 10−4 (8.5 × 10−6–2.5 × 10−4) 0.30 (0.26–0.53) 2.3 × 10−3 (2.3 × 10−4–4.6 × 10−3) 1.1 × 10−4 (2.8 × 10−6–1.9 × 10−4) 5.0 × 10−5
Group median data 3630 (3440–3835) 0.16 (0.06–0.34) 1.0 × 10−2 (1.4 × 10−5–2.0 × 10−2) 0.31 (0.09–0.47) 1.1 × 10−2 (7.4 × 10−3–1.4 × 10−2) 1.9 × 10−6 (4.1 × 10−7–3.3 × 10−6) 9.5 × 10−7
Slow-progressor morphine group
1/52N 3631 (3629–3632) 0.38 (0.31–0.47) 0.21 (0.08–0.35) 0.53 (0.44–0.63) 1.5 × 10−2 (1.2 × 10−2–1.8 × 10−2) 1.0 × 10−6 (1.3 × 10−7–2.0×10−6) 1.1 × 10−3
1/56L 3629 (3627–3631) 0.41 (0.28–0.62) 0.18 (0.04–0.34) 0.32 (0.24–0.36) 2.3 × 10−6 (1.5 × 10−7–4.4×10−6) 1.0 × 10−6 (6.8 × 10−8–1.8 × 10−6) 2.4 × 10−4
1/02N 3630 (3511–3757) 0.18 (0.15–0.22) 0.10 (0.02–0.18) 0.75 (0.55–0.96) 3.0 × 10−2 (1.2 × 10−2–4.8 × 10−2) 1.1 × 10−6 (2.6 × 10−8–1.9 × 10−6) 1.5 × 10−4
Group median data 3629 (3627–3630) 0.17 (0.11–0.22) 0.10 (0.02–0.21) 0.65 (0.42–0.68) 3.4 × 10−3 (1.0 × 10−3–5.5 × 10−3) 1.0 × 10−6 (3.3 × 10−7–2.6 × 10−6) 2.4 × 10−4
Control group
2/31P 3629 (3593–3661) 0.31 (0.23–0.41) 0.68 (0.51–0.91) 0.31 (0.24–0.34) 7.1 × 10−3 (5.5 × 10−3–1.0×10−2) 1.0 × 10−6 (1.1 × 10−7–2.0 × 10−6) 1.2 × 10−3
2/02P 4050 (3969–4125) 0.18 (0.13–0.24) 0.20 (0.10–0.34) 0.66 (0.40–0.74) 2.3 × 10−3 (7.1 × 10−4–4.4 × 10−3) 1.0 × 10−4 (3.7 × 10−5–2.0 × 10−4) 6.6 × 10−2
2/AC42 3630 (3627–3632) 0.14 (0.11–0.18) 0.33 (0.14–0.46) 0.54 (0.46–0.61) 5.3 × 10−4 (2.8 × 10−4–3.0 × 10−3) 4.9 × 10−6 (1.2 × 10−7–1.9 × 10−5) 2.2 × 10−2
MAC-1 3630 (3115–3893) 0.13 (0.10–0.25) 0.18 (0.07–0.29) 0.38 (0.16–0.39) 2.3 × 10−3 (3.0 × 10−4–3.4×10−3) 1.0 × 10−4 (1.4 × 10−5–1.5 × 10−4) 1.3 × 10−1
MAC-2 3629 (3610–3647) 0.13 (0.10–0.16) 0.28 (0.12–0.45) 0.61 (0.40–0.82) 3.2 × 10−6 (7.1×10−7–5.9 × 10−6) 1.0 × 10−7 (9.9 × 10−9–2.0 × 10−6) 1.4 × 10−4
MAC-3 3630 (3574–3684) 0.16 (0.08–0.29) 0.24 (0.06–0.43) 0.40 (0.24–0.53) 2.3 × 10−6 (1.4 × 10−7–4.6 × 10−6) 1.0 × 10−6 (5.9 × 10−8–2.0 × 10−6) 1.5 × 10−3
Group median data 3630 (3628–3631) 0.15 (0.12–0.19) 0.18 (0.07–0.31) 0.65 (0.41–0.81) 2.5 × 10−3 (1.1 × 10−3–4.4 × 10−3) 1.1 × 10−6 (2.2 × 10−7–2.7 × 10−6) 1.0 × 10−3