Simple models for complicated scenarios: Ebola in...
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Simple models for complicated scenarios: Ebola in West Africa Sarah B. Rainey 1 and John M. Drake 2 1 Radford University, Radford, VA 2 Odum School of Ecology, University of Georgia, Athens, Georgia Background Parameters Results Methods • Mathematical models are used for forecasting and decision making. • Predictions from models are subject to parameter and structural uncertainty. • Models produced early in the course of an epidemic tend to be simpler due to a lack of information with which to estimate parameters and an abbreviated development time. • Complex models are more cumbersome to develop but take into account more complex transmission scenarios reported by in-country observers. • Structural uncertainty is hardly ever assessed. It is important to quantify the level of structural uncertainty to mitigate model errors. • The 2014 Ebola outbreak in West Africa was used as a case study to investigate the level of structural uncertainty associated with simpler models. How well does a simple model accurately account for complicated scenarios involved in an infectious disease outbreak, such as Ebola? Table 1. Drake et al. Model Parameters -------------------------------------------------------------------------------- Parameters Values ---------------------------------------------------------------------------------- θ .01, .2, .4, .6, .8, 1.2 β 1, 2, 3, 5, 6, 8 ϕ .05, 1, 1.5, 2.5, 3 λ h .01, .05, .1, .2, .4, .5 α .001, .02, .04, .06, .08, .1 g .01, .1, .2, .5, .7, 1 h .01, .05, .1, .2, .4, .8 --------------------------------------------------------------------------------- • The following parameters were varied at the specified values to produce epidemics with alternative disease trajectories. • The statistical software R was used to solve three mathematical models. • A complex branching-process model published by Drake et al. (2015) was used to generate an Ebola epidemic with different scenarios by varying parameters. • Two simpler models, one published by Legrand et al. (2007) and the classical SIR model (Kermack and McKendrick, 1927) were fit to simulated data. • Legrand et al. (2007) • SIR (Kermack and McKendrick, 1927) • The correlation coefficient was calculated to test the fit of the models to observe how well they were able to capture the trajectory of the Ebola outbreak. S I R βΙ γ Research Question: Discussion References Acknowledgements: National Institutes of Health (NIH) Odum School of Ecology, University of Georgia Dr. John M. Drake (PI) and Drake Lab • The Legrand model was superior to the SIR model in the majority of the simulated epidemics. • The SIR model had a higher correlation coefficient than the Legrand model under the following circumstances: 1. θ = 0.8 2. β = 3 3. ϕ = 1.5 4. g = .5 5. h = .1 • Conclusion: In the case of the 2014 Ebola outbreak in West Africa, complex models that incorporated complicated scenarios had less structural uncertainty. 1. Drake, J. M., et al. (2015). Ebola Cases and Health System Demand in Liberia. PLOS Biology PLoS Biol, 13(1). doi:10.1371/journal.pbio.1002056. 2. Kermack, W. O. and McKendrick, A. G. "A Contribution to the Mathematical Theory of Epidemics." Proc. Roy. Soc. Lond. A 115, 700- 721, 1927. 3. Legrand, J., Grais, R., Boelle, P., Valleron, A., & Flahault, A. (2006). Understanding the dynamics of Ebola epidemics. Epidemiol. Infect. Epidemiology and Infection, 135(04), 610. doi:10.1017/s0950268806007217 Future Directions 1. Investigate the fit of the SIR and Legrand model to simulated epidemics of a combination of varied parameter values using the branching-process model published by Drake et al (2015) 2. Investigate the structural uncertainty of models for a different infectious disease • θ Manipulations • β Manipulations • ϕ Manipulations • λ h Manipulations • α Manipulations • g Manipulations • h Manipulations Theta CC - SIR CC - Legrand 0.01 0.597 0.8015 0.2 0.5434 0.8522 0.4 0.5813 0.9089 0.6 0.6197 0.8463 0.8 0.9782 0.9756 1.2 0.6335 0.9982 Alpha CC - SIR CC - Legrand 0.001 0.9884 0.9963 0.02 0.9897 0.9957 0.04 0.9609 0.9846 0.06 0.9771 0.9875 0.08 0.6372 0.9924 0.1 0.9752 0.9947 Beta CC - SIR CC - Legrand 1 0.9846 0.9976 2 0.9935 0.9993 3 0.9867 0.9807 5 0.9676 0.995 6 0.958 0.9916 8 0.9815 0.9954 g CC - SIR CC- Legrand 0.01 0.2794 0.7709 0.1 0.8511 0.9144 0.2 0.9894 0.9987 0.5 0.8901 0.8244 0.7 0.724 0.9547 1 0.7517 0.9577 Phi CC - SIR CC - Legrand .05 .6965 .9488 .5 .6200 .9532 1 .5976 .9379 1.5 .7880 .6852 2.5 .6195 .9974 3 .3545 .9209 h CC - SIR CC - Legrand 0.01 0.8909 0.9835 0.05 0.6924 0.7449 0.1 0.512 -0.0983 0.2 0.7337 0.8525 0.4 0.2374 0.9752 0.8 0.8252 0.9633 Lambda.h CC - SIR CC - Legrand 0.01 0.6625 0.9032 0.05 0.9127 0.9153 0.1 -0.302 0.7305 0.2 0.6163 0.8141 0.4 0.9928 0.9992 0.5 0.9935 0.9988
Transcript of Simple models for complicated scenarios: Ebola in...
Simple models for complicated scenarios: Ebola in West AfricaSarah B. Rainey1 and John M. Drake2
1 Radford University, Radford, VA2 Odum School of Ecology, University of Georgia, Athens, Georgia
Background Parameters
Results
Methods
• Mathematical models are used for forecasting and decision making.
• Predictions from models are subject to parameter and structural uncertainty.
• Models produced early in the course of an epidemic tend to be simpler due to a lack of information with which to estimate parameters and an abbreviated development time.
• Complex models are more cumbersome to develop but take into account more complex transmission scenarios reported by in-country observers.
• Structural uncertainty is hardly ever assessed. It is important to quantify the level of structural uncertainty to mitigate model errors.
• The 2014 Ebola outbreak in West Africa was used as a case study to investigate the level of structural uncertainty associated with simpler models.
How well does a simple model accurately account for
complicated scenarios involved in an infectious disease
outbreak, such as Ebola?
Table 1. Drake et al. Model Parameters--------------------------------------------------------------------------------
Parameters Values----------------------------------------------------------------------------------
θ .01, .2, .4, .6, .8, 1.2β 1, 2, 3, 5, 6, 8 ϕ .05, 1, 1.5, 2.5, 3λh .01, .05, .1, .2, .4, .5α .001, .02, .04, .06, .08, .1g .01, .1, .2, .5, .7, 1h .01, .05, .1, .2, .4, .8
---------------------------------------------------------------------------------
• The following parameters were varied at the specified values to produce epidemics with alternative disease trajectories.
• The statistical software R was used to solve three mathematical models.
• A complex branching-process model published by Drake et al. (2015) was used to generate an Ebola epidemic with different scenarios by varying parameters.
• Two simpler models, one published by Legrand et al. (2007) and the classical SIR model (Kermack and McKendrick, 1927) were fit to simulated data.
• Legrand et al. (2007)
• SIR (Kermack and McKendrick, 1927)
• The correlation coefficient was calculated to test the fit of the models to observe how well they were able to capture the trajectory of the Ebola outbreak.
S I RβΙ γ
Research Question:
Discussion
References
Acknowledgements: National Institutes of Health (NIH)Odum School of Ecology, University of GeorgiaDr. John M. Drake (PI) and Drake Lab
• The Legrand model was superior to the SIR model in the majority of the simulated epidemics.
• The SIR model had a higher correlation coefficient than the Legrand model under the following circumstances:
1. θ = 0.82. β = 33. ϕ = 1.54. g = .55. h = .1
• Conclusion: In the case of the 2014 Ebola outbreak in West Africa, complex models that incorporated complicated scenarios had less structural uncertainty.
1. Drake, J. M., et al. (2015). Ebola Cases and Health System Demand in Liberia. PLOS Biology PLoS Biol, 13(1). doi:10.1371/journal.pbio.1002056.
2. Kermack, W. O. and McKendrick, A. G. "A Contribution to the Mathematical Theory of Epidemics." Proc. Roy. Soc. Lond. A 115, 700-721, 1927.
3. Legrand, J., Grais, R., Boelle, P., Valleron, A., & Flahault, A. (2006). Understanding the dynamics of Ebola epidemics. Epidemiol. Infect. Epidemiology and Infection, 135(04), 610. doi:10.1017/s0950268806007217
Future Directions
1. Investigate the fit of the SIR and Legrand model to simulated epidemics of a combination of varied parameter values using the branching-process model published by Drake et al (2015)
2. Investigate the structural uncertainty of models for a different infectious disease
• θ Manipulations
• β Manipulations
• ϕ Manipulations
• λh Manipulations
• α Manipulations
• g Manipulations
• h Manipulations
Theta CC - SIR CC - Legrand0.01 0.597 0.80150.2 0.5434 0.85220.4 0.5813 0.90890.6 0.6197 0.84630.8 0.9782 0.97561.2 0.6335 0.9982
Alpha CC - SIR CC - Legrand0.001 0.9884 0.99630.02 0.9897 0.99570.04 0.9609 0.98460.06 0.9771 0.98750.08 0.6372 0.99240.1 0.9752 0.9947
Beta CC - SIR CC - Legrand1 0.9846 0.99762 0.9935 0.99933 0.9867 0.98075 0.9676 0.9956 0.958 0.99168 0.9815 0.9954
g CC - SIR CC- Legrand
0.01 0.2794 0.77090.1 0.8511 0.91440.2 0.9894 0.99870.5 0.8901 0.82440.7 0.724 0.95471 0.7517 0.9577
Phi CC - SIR CC - Legrand.05 .6965 .9488.5 .6200 .95321 .5976 .9379
1.5 .7880 .68522.5 .6195 .99743 .3545 .9209
h CC - SIR CC - Legrand0.01 0.8909 0.98350.05 0.6924 0.74490.1 0.512 -0.09830.2 0.7337 0.85250.4 0.2374 0.97520.8 0.8252 0.9633
Lambda.h CC - SIR CC - Legrand0.01 0.6625 0.90320.05 0.9127 0.91530.1 -0.302 0.73050.2 0.6163 0.81410.4 0.9928 0.99920.5 0.9935 0.9988
