Developing a Novel Parameter Estimation Method for Agent-Based Model in Immune System Simulation under the Framework of History Matching: A Case Study on Influenza A Virus Infection
Abstract
:1. Introduction
2. Results and Discussion
2.1. Observation Data of Influenza A Virus (IAV)
2.2. Sampling Data
2.3. Non-Implausible Space
2.4. Fitting Experimental Data
2.5. Average Relative Error
3. Methods
3.1. Simulator: Using ABM (Agent-based Model) to Simulate the Immune System
3.2. Emulator: GAM Model
3.3. Reducing the Input Space by Using Implausibility Measure
3.4. Parameter Estimation
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Time Points (Day−1) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Samples | 0 | 0.125 | 0.25 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |
1 | 4.25 | 2.5 | 3.5 | 4.25 | 5.5 | 6.5 | 6.33 | 6.75 | 6.5 | 6.5 | 6.5 | 7 | 6.33 |
2 | 3.75 | 2.5 | 4.75 | 3.25 | 6.75 | 6.75 | 7.5 | 3.5 | 7.33 | 7.25 | 6.25 | 6.5 | 5.5 |
3 | 4.25 | 3.5 | 4.75 | 5.25 | 6.5 | 7.75 | 7.75 | 7.5 | 7.33 | 7.25 | 6.5 | 6.25 | 5.75 |
4 | 3.75 | 3.5 | 4.13 | 5.75 | 7.25 | NA | 7.25 | 6.5 | 6.25 | 5.5 | NA | NA | NA |
5 | 4.55 | 2.75 | 2.5 | 5.75 | NA | NA | NA | 7.5 | 6.75 | 6.5 | NA | NA | NA |
6 | 4.25 | NA | 4.75 | 5.5 | NA | NA | NA | NA | 7.25 | 5.75 | NA | NA | NA |
Samples | ||||
---|---|---|---|---|
1 | 3.466758 × 10−9 | 2.288938 × 10−7 | 2.460326 × 10−2 | 8.616152 × 10−2 |
2 | 8.001264 × 10−9 | 4.300130 × 10−7 | 8.741329 × 10−2 | 3.955367 × 10−1 |
3 | 1.081166 × 10−8 | 1.932323 × 10−7 | 1.004010 × 10−1 | 3.100995 × 10−1 |
4 | 1.090549 × 10−8 | 2.812863 × 10−7 | 8.654013 × 10−2 | 3.202220 × 10−1 |
5 | 9.102252 × 10−9 | 4.513295 × 10−7 | 4.608862 × 10−2 | 1.196989 × 10−1 |
6 | 3.405003 × 10−9 | 3.370440 × 10−8 | 1.130993 × 10−1 | 6.104288 × 10−1 |
7 | 8.092254 × 10−9 | 4.017315 × 10−8 | 2.174145 × 10−2 | 2.430601 × 10−1 |
8 | 2.010234 × 10−9 | 1.745676 × 10−8 | 6.418247 × 10−2 | 1.722317 × 10−1 |
9 | 1.691198 × 10−9 | 3.527068 × 10−7 | 1.158533 × 10−1 | 1.302177 × 10−2 |
10 | 2.912003 × 10−9 | 2.957414 × 10−7 | 2.715800 × 10−2 | 2.602361 × 10−1 |
11 | 2.554265 × 10−9 | 9.798854 × 10−8 | 1.866300 × 10−2 | 5.577698 × 10−1 |
12 | 6.864842 × 10−9 | 4.184238 × 10−7 | 1.079778 × 10−1 | 7.730243 × 10−1 |
13 | 1.121311 × 10−9 | 3.102666 × 10−7 | 2.784293 × 10−3 | 5.343298 × 10−2 |
14 | 9.583759 × 10−9 | 6.668325 × 10−8 | 3.832125 × 10−2 | 7.836137 × 10−1 |
15 | 8.762499 × 10−9 | 5.740286 × 10−8 | 6.656615 × 10−2 | 1.462840 × 10−1 |
16 | 1.167708 × 10−8 | 1.339571 × 10−7 | 1.286682 × 10−2 | 7.554816 × 10−1 |
17 | 5.319678 × 10−9 | 4.057522 × 10−7 | 7.242679 × 10−2 | 6.884958 × 10−1 |
18 | 7.634766 × 10−9 | 8.162650 × 10−8 | 9.417931 × 10−2 | 8.124229 × 10−1 |
19 | 9.973253 × 10−9 | 1.641823 × 10−7 | 5.553776 × 10−2 | 1.506380 × 10−1 |
20 | 6.455279 × 10−9 | 1.729994 × 10−7 | 7.591240 × 10−2 | 4.765285 × 10−1 |
21 | 3.989849 × 10−9 | 9.193181 × 10−8 | 9.013124 × 10−2 | 4.137486 × 10−1 |
22 | 1.212724 × 10−8 | 4.454997 × 10−7 | 1.593432 × 10−2 | 1.957182 × 10−1 |
23 | 9.163350 × 10−10 | 3.647394 × 10−7 | 7.019446 × 10−2 | 5.823037 × 10−1 |
24 | 4.437117 × 10−9 | 3.801312 × 10−7 | 8.076542 × 10−3 | 6.162935 × 10−1 |
25 | 1.186253 × 10−8 | 3.221797 × 10−7 | 6.068513 × 10−2 | 2.227833 × 10−1 |
26 | 5.134477 × 10−9 | 2.635175 × 10−7 | 9.752898 × 10−2 | 5.182151 × 10−1 |
27 | 4.222250 × 10−9 | 2.151502 × 10−7 | 1.059426 × 10−1 | 8.356908 × 10−1 |
28 | 1.246306 × 10−9 | 3.445810 × 10−7 | 5.116530 × 10−2 | 4.604467 × 10−1 |
29 | 1.134631 × 10−8 | 1.157556 × 10−7 | 3.036958 × 10−2 | 6.538406 × 10−1 |
30 | 2.343542 × 10−9 | 1.483302 × 10−7 | 7.804259 × 10−2 | 4.427248 × 10−1 |
31 | 4.911390 × 10−9 | 1.124756 × 10−8 | 1.018424 × 10−1 | 2.351053 × 10−2 |
32 | 1.043893 × 10−8 | 4.616473 × 10−7 | 5.736185 × 10−2 | 2.911685 × 10−1 |
33 | 5.792641 × 10−9 | 4.757734 × 10−7 | 1.195959 × 10−1 | 7.008772 × 10−1 |
34 | 7.162705 × 10−9 | 1.314465 × 10−7 | 1.195076 × 10−2 | 3.444968 × 10−1 |
35 | 6.743423 × 10−9 | 2.437133 × 10−7 | 5.718468 × 10−3 | 6.614001 × 10−2 |
36 | 8.583690 × 10−9 | 3.363820 × 10−7 | 3.510043 × 10−2 | 4.877613 × 10−1 |
37 | 1.832510 × 10−10 | 1.983512 × 10−7 | 4.478183 × 10−2 | 3.777456 × 10−1 |
38 | 5.980517 × 10−9 | 3.927292 × 10−7 | 4.956199 × 10−2 | 6.684690 × 10−1 |
39 | 5.754720 × 10−10 | 2.763359 × 10−7 | 4.084022 × 10−2 | 5.291611 × 10−1 |
40 | 9.649890 × 10−9 | 2.419316 × 10−7 | 8.210135 × 10−2 | 7.266126 × 10−1 |
Parameters | Initial Interval | Non-Implausible Interval |
---|---|---|
[0, 1.240000 × 10−8] | [3.8139 × 10−14, 1.2400 × 10−8] | |
[0, 4.840000 × 10−7] | [2.5844 × 10−14, 4.8400 × 10−7] | |
[0, 1.196000 × 10−1] | [8.7906 × 10−7, 1.1960 × 10−1] | |
[0, 8.460000 × 10−1] | [6.1473 × 10−6, 8.4600 × 10−1] |
Parameters | ||||
---|---|---|---|---|
Model | ||||
Initial Parameters | 6.2000 × 10−9 | 2.4200 × 10−7 | 5.9800 × 10−2 | 4.2300 × 10−1 |
Our Estimates | 6.5656 × 10−9 | 7.2467 × 10−9 | 2.7739 × 10−2 | 1.2595 × 10−1 |
(4.2290 × 10−9) | (6.4759 × 10−11) | (2.8178 × 10−7) | (3.1538 × 10−6) |
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Li, T.; Cheng, Z.; Zhang, L. Developing a Novel Parameter Estimation Method for Agent-Based Model in Immune System Simulation under the Framework of History Matching: A Case Study on Influenza A Virus Infection. Int. J. Mol. Sci. 2017, 18, 2592. https://doi.org/10.3390/ijms18122592
Li T, Cheng Z, Zhang L. Developing a Novel Parameter Estimation Method for Agent-Based Model in Immune System Simulation under the Framework of History Matching: A Case Study on Influenza A Virus Infection. International Journal of Molecular Sciences. 2017; 18(12):2592. https://doi.org/10.3390/ijms18122592
Chicago/Turabian StyleLi, Tingting, Zhengguo Cheng, and Le Zhang. 2017. "Developing a Novel Parameter Estimation Method for Agent-Based Model in Immune System Simulation under the Framework of History Matching: A Case Study on Influenza A Virus Infection" International Journal of Molecular Sciences 18, no. 12: 2592. https://doi.org/10.3390/ijms18122592