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Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

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  • Daniel P Word
  • James K Young
  • Derek A T Cummings
  • Sopon Iamsirithaworn
  • Carl D Laird

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.

Suggested Citation

  • Daniel P Word & James K Young & Derek A T Cummings & Sopon Iamsirithaworn & Carl D Laird, 2013. "Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:plo:pone00:0074208
    DOI: 10.1371/journal.pone.0074208
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    References listed on IDEAS

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    1. William E. Hart & Carl Laird & Jean-Paul Watson & David L. Woodruff, 2012. "Pyomo – Optimization Modeling in Python," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-3226-5, December.
    2. B. F. Finkenstädt & B. T. Grenfell, 2000. "Time series modelling of childhood diseases: a dynamical systems approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(2), pages 187-205.
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