(625aa) Parallel Decomposition Strategies for Estimation of a Spatially Distributed, Nonlinear, Childhood Infectious Disease Model | AIChE

(625aa) Parallel Decomposition Strategies for Estimation of a Spatially Distributed, Nonlinear, Childhood Infectious Disease Model

Authors 

Watson, J. P. - Presenter, Sandia National Laboratories
Woodruff, D. L. - Presenter, University of California, Davis


Understanding the factors that influence the dynamics of childhood infectious diseases is important for developing effective methods of controlling and reducing disease spread.  The development of reliable, accurate mathematical models has been useful to help identify and understand factors that contribute to disease dynamics, but the accuracy of these models depend upon appropriate model parameter values which are unknown and must be estimated from available data.

            Previously, we have shown efficient techniques to estimate seasonal transmission parameters using discrete-time and continuous-time infectious disease models.  These models are formulated using differential equations and, using the simultaneous discretization approach, give rise to large-scale nonlinear optimization problems for estimating transmission parameters in large cities where diseases are endemic.  However, in smaller cities fadeout is often observed making estimation much more difficult.  For example, it has been shown that in urban areas larger than around 300,000 people, without the influence of vaccination, measles is self-sustaining.  Since the population in many areas is significantly below this critical community size, stochastic fadeout is commonly seen and can cause extended periods of time with no observed cases.  Cases are observed again only after an infection is imported from outside the community.  To reasonably estimate disease transmission parameters in these smaller communities, and to better understand the factors behind this spatial coupling, the importation of new cases between cities must be considered.  This can be done by including a spatial component in the model that includes information about the geographic location and population of communities.  However, parameter estimations using long time horizons and spatial components with many cities create nonlinear estimation problems that can be intractably large for general estimation approaches.

            In this work, we demonstrate an effective solution approach for estimating transmission parameters in a continuous time, spatially distributed infectious disease model using both progressive hedging and internal linear decomposition.  These decomposition techniques enable parallel solution of these large-scale nonlinear optimization problems. We demonstrate our approach using measles incidence data from 60 cities in England and Wales, and measles incidence data from the 72 provinces of Thailand. This solution approach allows efficient solution for large problems and shows good scalability with problem size.