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. 2013 Oct 22;8(10):e74208.
doi: 10.1371/journal.pone.0074208. eCollection 2013.

Interior-point methods for estimating seasonal parameters in discrete-time infectious disease models

Daniel P Word  1 , James K Young, Derek A T Cummings, Sopon Iamsirithaworn, Carl D Laird
Affiliations

Interior-point methods for estimating seasonal parameters in discrete-time infectious disease models

Daniel P Word et al. PLoS One. .

Abstract

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The true values of used in the SIR simulation study (circles).
The mean of the estimates from the simulation study (solid line). The 2.5th and 97.5th quantiles of the estimates from the simulation study (dashed lines).
Figure 2
Figure 2. The estimated transmission profile (solid line) for a single data set with 95% confidence intervals (– –) found using log-likelihoods as described in .
The true values of formula image used in the SIR simulation (circles).
Figure 3
Figure 3. A comparison of seasonal transmission parameters estimated for London.
The values estimated in this work (– –) are overlaid with those reported by Finkenstädt and Grenfell (—).
Figure 4
Figure 4. New York City results: The estimated number of reported cases (– –) with the actual number of reported cases (—) of measles.
Figure 5
Figure 5. New York City results: The estimated number of individuals susceptible to measles.
Figure 6
Figure 6. Estimated for measles in New York City with 95 confidence intervals (—).
Figure 7
Figure 7. New York City results: 95 confidence region for and .
Figure 8
Figure 8. New York City results: 95 confidence region for and .
Figure 9
Figure 9. New York City results: 95 confidence region for and .
Figure 10
Figure 10. Bangkok results: The estimated number of reported cases (– –) with the actual number of reported cases (—) of measles.
Note: Case data is unavailable for 1979.
Figure 11
Figure 11. Estimated for measles in Bangkok with 95 confidence intervals (–).
Figure 12
Figure 12. New York City estimates of seasonal exponential parameter with 95 confidence intervals.
Figure 13
Figure 13. Bangkok estimates of seasonal exponential parameter with 95 confidence intervals.
Figure 14
Figure 14. Spearman correlation coefficients computed for New York City are shown.
The coefficient calculated using reported holiday schedules and estimated parameters are shown by the dashed line. The coefficient computed using a holiday schedule shifted forward by one biweek is shown by the solid line. The histogram shows the distribution of correlations that were computed between the reported holiday schedule and 1,000 randomly ordered vectors of our parameter estimates.
Figure 15
Figure 15. Spearman correlation coefficients computed for Bangkok are shown.
The coefficient calculated using reported holiday schedules and estimated parameters are shown by the dashed line. The coefficient computed using a holiday schedule shifted forward by one biweek is shown by the solid line. The histogram shows the distribution of correlations that were computed between the reported holiday schedule and 1,000 randomly ordered vectors of our parameter estimates.
Figure 16
Figure 16. New York City estimates of seasonal weight on births, .
Figure 17
Figure 17. Bangkok estimates of seasonal weight on births, .
See this image and copyright information in PMC

References

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