Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence
Abstract
:1. Introduction
2. Data, Modelling Methods and Analysis Tools
2.1. Empirical Series of Malaria Incidence
2.2. Agent Model for Malarial Spreading
2.3. Hurst Exponent and Entropy to Assess Memory Effects in Stochastic Series
2.4. Estimating the Hurst Exponent and Entropy in Series of Malaria Incidence
3. Qualitative Analysis and Robustness Assessment of the Hurst Exponent and Entropy in Empirical Time Series Behavior
4. Autocorrelation Function and Stochastic Memory in Malaria Empirical Series
5. Towards a More Quantitative Malaria Model for Predicting Effective Gametocytemia
5.1. Models for the Three Observables as Function of Parameter Gametocytemia
5.2. Prediction of Effective Gametocytemia for Empirical Cases
6. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Qualitative Analysis of Hurst Exponent and Entropy: Case-by-Case Description
Appendix A.1. Alhassan (2017)
Appendix A.2. Appiah (2015)
Appendix A.3. Bedane (2016)
Appendix A.4. Aregawi (2014)
Appendix A.5. Gomez-Elipe (2007)
Appendix A.6. Muwanika (2017)
Appendix A.7. Landoh (2012)
Appendix A.8. Okech (2008)
Appendix B. Inspecting the Robustness of 36-Month Averages
Empirical Series | GHE for | GHE for |
---|---|---|
Aregawi [22] | 0.48 | 0.49 |
Alhassan [21] | 0.48 | 0.56 |
Bedane [23] | 0.73 | 0.48 |
Appiah [16] | 0.21 | 0.09 |
Landoh [25] | 0.65 | 0.62 |
Muwanika [26] | 0.41 | 0.37 |
Elipe [24] | 0.73 | 0.60 |
Okech [27] | 0.26 | 0.42 |
Appendix C. Arima Models of the Incidence of Malaria
Level | Malaria Transmission Intensity | Malaria Incidence (±SE) | ||
---|---|---|---|---|
Low | 0.420 | Phase transition | 7.7 (±0.89) | |
High | 0.733 | Epidemic stability | 169.7 (±0.64) | |
Series | Follow-Up (months) | Region | Trend | Malaria incidence (±SD) |
Okech, 2008 | 96 | Kenya | decreasing | 205.1 (±169.8) |
Landoh, 2012 | 72 | Togo | increasing | 24.4 (±11.5) |
SARIMA | Model | |
---|---|---|
0.420 | ||
0.733 | ||
0.420 | 0.733 | |
−0.3635 | −0.3495 | |
0.3415 | −0.2344 | |
−0.3455 | −0.2997 | |
−0.5422 | −0.2221 | |
0.6564 | −0.2273 | |
−0.1574 | −0.7408 | |
−1.4685 | – | |
0.7626 | – | |
(drift) | – | – |
10.89 | 1037 | |
AICc | 1849.32 | 3426.29 |
Empirical Series | SARIMA | |
---|---|---|
Okech, 2008 | ||
Landoh, 2012 | ||
Okech, 2008 | Landoh, 2012 | |
0.6357 | 0.5306 | |
−0.8778 | −1.000 | |
– | −0.4894 | |
−0.6522 | – | |
2518 | 17.49 | |
AICc | 900.8 | 351.15 |
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Empirical Series | Year | I 36 Months () | H 36 Months () | S 36 Months () | Duration Months |
---|---|---|---|---|---|
Aregawi [22] | 2014 | 0.208 ± 0.0495 | 0.7766 ± 0.1428 | 5.138 ± 0.0064 | 132 |
Alhassan [21] | 2017 | 7.091 ± 2.808 | 1.014 ± 0.1425 | 4.792 ± 0.1717 | 72 |
Bedane [23] | 2016 | 11.63 ± 1.355 | 1.077 ± 0.0925 | 5.161 ± 0.0036 | 120 |
Appiah [16] | 2015 | 12.44 ± 0.1318 | 0.9229 ± 0.0570 | 5.121 ± 0.0026 | 60 |
Landoh [25] | 2012 | 24.54 ± 4.312 | 0.7326 ± 0.0850 | 5.065 ± 0.0206 | 72 |
Muwanika [26] | 2017 | 58.76 ± 1.112 | 0.8254 ± 0.1236 | 5.160 ± 0.0027 | 71 |
Elipe [24] | 2007 | 101.0 ± 28.20 | 0.9367 ± 0.0993 | 4.710 ± 0.1733 | 84 |
Okech [27] | 2008 | 203.4 ± 120.2 | 1.018 ± 0.1568 | 4.881 ± 0.2774 | 96 |
Empirical Series | () Median | () | () | () Median | () | () | () Median | () | () |
---|---|---|---|---|---|---|---|---|---|
Aregawi, 2014 | 0.22 | 0.16 | 0.26 | 0.80 | 0.66 | 0.90 | 5.14 | 5.13 | 5.14 |
Alhassan, 2017 | 7.43 | 4.36 | 9.68 | 0.94 | 0.90 | 1.15 | 4.77 | 4.68 | 4.96 |
Bedane, 2016 | 11.2 | 10.4 | 12.4 | 1.10 | 1.00 | 1.15 | 5.16 | 5.16 | 5.16 |
Appiah, 2015 | 12.5 | 12.4 | 12.5 | 0.93 | 0.87 | 0.96 | 5.12 | 5.12 | 5.12 |
Landoh, 2012 | 24.0 | 21.0 | 28.4 | 0.76 | 0.70 | 0.80 | 5.06 | 5.05 | 5.08 |
Muwanika, 2017 | 59.0 | 58.2 | 59.7 | 0.81 | 0.77 | 0.90 | 5.16 | 5.16 | 5.16 |
Elipe, 2007 | 115 | 83.5 | 122 | 0.95 | 0.89 | 1.00 | 4.67 | 4.59 | 4.72 |
Okech, 2008 | 211 | 89.1 | 310 | 1.06 | 0.98 | 1.13 | 4.96 | 4.85 | 5.08 |
Average | 24 Months | 36 Months | 48 Months | |||
---|---|---|---|---|---|---|
Pearson coeff. | ||||||
Aregawi, 2014 [22] | 0.048 | 0.216 | 0.323 | 0.223 | 0.727 | 0.012 |
Alhassan, 2017 [21] | 0.528 | 0.657 | 0.638 | 0.879 | 0.530 | 0.746 |
Bedane, 2016 [23] | 0.006 | 0.107 | 0.094 | 0.027 | 0.000 | 0.181 |
Appiah, 2015 [16] | 0.336 | 0.620 | 0.222 | 0.353 | 0.299 | 0.534 |
Landoh, 2012 [25] | 0.310 | 0.339 | 0.436 | 0.633 | 0.722 | 0.743 |
Muwanika, 2017 [26] | 0.043 | 0.547 | 0.175 | 0.748 | 0.449 | 0.903 |
Elipe, 2007 [24] | 0.074 | 0.886 | 0.012 | 0.655 | 0.590 | 0.683 |
Okech, 2008 [27] | 0.068 | 0.603 | 0.414 | 0.069 | 0.013 | 0.949 |
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Sequeira, J.; Louçã, J.; Mendes, A.M.; Lind, P.G. Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence. Appl. Sci. 2022, 12, 496. https://doi.org/10.3390/app12010496
Sequeira J, Louçã J, Mendes AM, Lind PG. Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence. Applied Sciences. 2022; 12(1):496. https://doi.org/10.3390/app12010496
Chicago/Turabian StyleSequeira, João, Jorge Louçã, António M. Mendes, and Pedro G. Lind. 2022. "Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence" Applied Sciences 12, no. 1: 496. https://doi.org/10.3390/app12010496
APA StyleSequeira, J., Louçã, J., Mendes, A. M., & Lind, P. G. (2022). Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence. Applied Sciences, 12(1), 496. https://doi.org/10.3390/app12010496