(456d) A Nonlinear Programming Framework for Estimating Spatial Coupling and Seasonal Transmission Parameters in Disease Transmission

Highly infectious pathogens can cause localized outbreaks that are followed by regional extinction as susceptible hosts are exhausted. Spatial transmission of these pathogens can once again spark new outbreaks. Study of spatial transmission parameters is essential to predicting and mitigating these outbreaks, as well as quantifying disease persistence within a large population.

We address the issue of estimating disease transmission parameters using a flexible, scalable modeling framework. Spatial coupling parameters are a measure of the level of mixing of individuals between regional subpopulations [1]. Seasonal transmission parameters describe the impact of seasonal variation due to effects like degree of interaction [2]. This work focuses on estimating both spatial coupling and seasonal transmission parameters with a nonlinear programming approach for a network of subpopulations.

A framework is presented for efficient estimation of city-to-city spatial transmission rates by inferring transport information from localized disease case data using a statistical, hazard-based SIR model [3]. The estimation is demonstrated using records of measles outbreaks in 954 cities across England and Wales between 1944 and 1964. First, a stochastic model is constructed to predict spatio-temporal disease dynamics and accurately match existing datasets. A statistical hazard-based approach focusing on disease fade-out periods provides the basis for the estimation. Then, the model is extended to simultaneously estimate the city-to-city spatial transmission parameters, as well as seasonal transmission parameters. The proposed approach for this large-scale estimation accurately reproduces existing parameter estimates from [1,4], is readily scalable to larger problem sizes, and substantially reduces solution times.

References:

[1] Bjørnstad, O. N. and Grenfell, B. T. (2008). Hazards, spatial transmission and timing of outbreaks in epidemic metapopulations. Environmental and Ecological Statistics, 15:265–277.

[2] Word, D. P., Cummings, D. a. T., Burke, D. S., Iamsirithaworn, S., and Laird, C. D. (2012). A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model. Journal of the Royal Society, Interface / the Royal Society, 9:1983–97.

[3] Grenfell, B. T. (2000). Time series modelling of childhood diseases: a dynamical systems approach. Appl. Statist.

[4] Xia, Y., Bjørnstad, O. N., and Grenfell, B. T. (2004). Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. The American naturalist, 164(2):267–281.