(245d) A Nonlinear Programming Framework for Estimating Spatial Coupling in Disease Transmission

This work addresses the issue of estimating disease transmission parameters using a flexible, scalable modeling framework. Highly infectious pathogens can cause significant outbreaks that are followed by regional extinctions as they run out of susceptible hosts within a population. Rescue effects due to spatial transmission of these pathogens can once again spark epidemics and lead to disease persistence within subpopulations [1]. Spatial coupling parameters are a measure of the level of mixing of individuals between these subpopulations [2]. Computational models have become essential for understanding epidemiological patterns and developing the evidence base for decision-making, but require accurate estimates of the parameters that enter into the models. Furthermore, it is important that the computational modeling framework be flexible and readily scalable to larger problem sizes [3]. This work focuses on quantifying rates of disease transmission for a network of subpopulations by estimating their spatial coupling parameters with a nonlinear programming approach.

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 [4]. 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 provided the basis for the estimation [2]. Subsequently, the strength of city-to-metapopulation spatial transmission is estimated using disease fade-out information between outbreaks. Then, the model is extended to estimate the strength of city-to-city spatial transmission [5]. The estimation is demonstrated using various records of datasets for measles outbreaks. The proposed approach is found to be feasible for this large-scale estimation, and accurately reproduces existing literature values. Additionally, the proposed approach for estimating disease transmission parameters is flexible, and allows for further investigation of larger model spaces.

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[2] Bjø rnstad, O. N. and Grenfell, B. T. (2008). Hazards, spatial transmission and timing of outbreaks in epidemic metapopulations. Environmental and Ecological Statistics, 15:265â??277.

[3] 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, 9:1983â??97.

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

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