Table 2. Antibody acquisition model parameter estimates.
| Antigen | Model | α0 | γ | r | tc | σ | Log-likelihood | AIC |
|---|---|---|---|---|---|---|---|---|
| AMA-1_3D7 | M1 | 0.27 (0.24, 0.34) | – | 0.0 (0.0, 0.03) | – | 2.18 (2.06, 2.29) | −2026.17 | 4058.35 |
| M2 | 0.89 (0.66, 1.32) | 0.09 (0.07, 0.14) | 0.0 (0.0, 0.05) | 1998 (1997, 1999) | 1.92 (1.82, 2.02) | −1942.73 | 3895.45 | |
| M3 | 1.55 (0.91, 2.72) | 0.009(0.001,0.04) | 0.10 (0.01, 0.20) | – | 1.97 (1.88, 2.08) | −1961.93 | 3931.85 | |
| AMA-1_FVO | M1 | 0.28 (0.24, 0.34) | – | 0.0 (0.0, 0.02) | – | 2.23 (2.11, 2.35) | −2052.93 | 4111.85 |
| M2 | 0.95 (0.66, 1.47) | 0.08 (0.06, 0.12) | 0.0 (0.0, 0.06) | 1998 (1997, 2000) | 1.93 (1.81, 2.06) | −1957.98 | 3925.96 | |
| M3 | 1.48 (0.72, 2.53) | 0.003(0.001,0.03) | 0.08 (0.0, 0.18) | – | 2.00 (1.91, 2.11) | −1980.09 | 3968.18 | |
| MSP-119 | M1 | 0.47 (0.34, 0.71) | – | 0.07 (0.0, 0.18) | – | 1.67 (1.59, 1.77) | −1998.72 | 4003.44 |
| M2 | 7.8. (1.2, 45.5) | 0.084 (0.016, 0.28) | 0.23 (0.02, 0.45) | 1991 (1988, 2002) | 1.64 (1.55, 1.72) | −1987.69 | 3985.38 | |
| M3 | 1.19 (0.71, 2.01) | 0.29 (0.17, 0.49) | 0.13 (0.05, 0.25) | – | 1.65 (1.57, 1.74) | −1988.70 | 3985.40 | |
| MSP-2_Dd2 | M1 | 0.50 (0.44, 0.59) | – | 0.0 (0.0, 0.02) | – | 2.03 (1.92, 2.14) | −2381.28 | 4768.56 |
| M2 | 1.96 (1.56, 2.92) | 0.08 (0.06, 0.11) | 0.0 (0.0, 0.05) | 1997 (1996, 1998) | 1.70 (1.61, 1.81) | −2263.92 | 4537.84 | |
| M3 | 3.37 (2.02, 5.58) | 0.002 (0.001,0.2) | 0.12 (0.04, 0.22) | – | 1.79 (1.69, 1.88) | −2296.06 | 4600.12 | |
| MSP-2_CH150/9 | M1 | 0.58 (0.49, 0.71) | – | 0.0 (0.0, 0.02) | – | 2.26 (2.14, 2.39) | −2562.06 | 5130.12 |
| M2 | 1.95 (1.52, 3.28) | 0.08 (0.06, 0.11) | 0.0 (0.0, 0.06) | 1998 (1997, 1999) | 1.95 (1.84, 2.06) | −2463.86 | 4937.71 | |
| M3 | 3.64 (2.13, 6.37) | 0.0 (0.0, 0.02) | 0.11 (0.02, 0.21) | – | 2.01 (1.91, 2.11) | −2483.66 | 4975.31 | |
| MSP-3_3D7 | M1 | 6.80 (4.53, 12.97) | – | 0.34 (0.19, 0.72) | – | 1.17 (1.12, 1.24) | −2976.95 | 5959.90 |
| M2 | 29.98 (3.0,100) | 0.08 (0.07,0.15) | 0.35 (0.31,0.48) | 1992 (1990, 1993) | 1.15 (1.10,1.22) | −2966.78 | 5943.55 | |
| M3 | 10.59 (6.18, 22.8) | 0.59 (0.42, 0.86) | 0.38 (0.22, 0.79) | – | 1.16 (1.10, 1.24) | −2973.43 | 5954.87 | |
| MSP-3_K1 | M1 | 1.20 (0.84, 1.89) | – | 0.06 (0.0, 0.17) | – | 1.81 (1.71, 1.90) | −2706.36 | 5418.72 |
| M2 | 2.90 (1.87, 6.69) | 0.28 (0.18, 0.39) | 0.10 (0.03, 0.22) | 1998 (1996, 2001) | 1.73 (1.63, 1.82) | −2675.38 | 5360.75 | |
| M3 | 4.99 (3.07, 9.0) | 0.14 (0.07, 0.23) | 0.17 (0.09, 0.33) | – | 1.74 (1.65, 1.84) | −2680.85 | 5369.70 | |
| gSG6 | M1 | 18.2 (12.7, 32.1) | – | 0.82 (0.55, 1.50) | – | 0.69 (0.65, 0.73) | −2677.39 | 5360.78 |
| M2 | 27.6 (17.1, 39.4) | 0.64 (0.42,0.75) | 1.02 (0.60,1.50) | 2008 (1997, 2009) | 0.66 (0.63,0.71) | −2651.88 | 5313.75 | |
| M3 | 37.25 (23.9, 42.5) | 0.46 (0.38, 0.55) | 0.96 (0.65, 1.19) | – | 0.66 (0.63, 0.71) | −2652.21 | 5312.41 |
Maximum likelihood parameter estimates and 95% confidence intervals for antibody acquisition models fitted to cross-sectional antibody levels data. α0 is the rate of antibody boosting, γ (= αc/α0) is the reduction in transmission, r is the rate of antibody decay, tc is the estimated time-point (calendar year) of drop in transmission, σ is the standard deviation of the antibody levels on the log scale, log-likelihood is the maximised log-likelihood of the model and AIC is the Akaike Information Criterion value. A bold font indicates the smallest AIC for each of the antigens. Confidence Intervals were defined using profile-likelihood methods.