Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach

This paper is concerned with the modeling of infectious disease spread in a composite space-time domain under conditions of uncertainty. We focus on stochastic modeling that accounts for basic mechanisms of disease distribution and multi-sourced in situ uncertainties. Starting from the general formulation of population migration dynamics and the specification of transmission and recovery rates, the model studies the functional formulation of the evolution of the fractions of susceptible-infected-recovered individuals. The suggested approach is capable of: a) modeling population dynamics within and across localities, b) integrating the disease representation (i.e. susceptible-infected-recovered individuals) with observation time series at different geographical locations and other sources of information (e.g. hard and soft data, empirical relationships, secondary information), and c) generating predictions of disease spread and associated parameters in real time, while considering model and observation uncertainties. Key aspects of the proposed approach are illustrated by means of simulations (i.e. synthetic studies), and a real-world application using hand-foot-mouth disease (HFMD) data from China.J.M. Angulo and A.E. Madrid have been partially supported by grants MTM2009-13250 and MTM2012-32666 of SGPI, and P08-FQM-3834 of the Andalusian CICE, Spain. H-L Yu has been partially supported by a grant from National Science Council of Taiwan (NSC101-2628-E-002-017-MY3 and NSC102-2221-E-002-140-MY3). A. Kolovos was supported by SpaceTimeWorks, LLC. G. Christakos was supported by a Yongqian Chair Professorship (Zhejiang University, China)

Comparison of the temporal evolution of infected (solid lines), susceptible (dashed lines), and recovered (dotted lines) population fractions at a certain location in terms of (a) the temporal variation of purely temporal model (red color), and the spatiotemporal model for two different kernel bandwidth values (blue), 3 (green).

<p>The probability of recovery is set to ; the probability of transmission is , and the population fraction that resides inside the domain of interest is , and (b) the associated simplex triangle plot.</p

Comparison of the temporal evolution of infected (solid lines), susceptible (dashed lines), and recovered (dotted lines) population fractions at a certain location in terms of (a) the temporal variation with different values of the probability of recovery (red color), 0.4 (blue), 0.6 (green).

<p>The probability of transmission is , the population fraction that resides inside the domain of interest is , and the kernel bandwidth is , and (b) the associated simplex triangle plot.</p

Comparison between the simulated and estimated recovery rates using the exKF and BME-SIR methods.

<p>Comparison between the simulated and estimated recovery rates using the exKF and BME-SIR methods.</p

BME-SIR estimated transmission and recovery rates in the HFMD study.

<p>BME-SIR estimated transmission and recovery rates in the HFMD study.</p

Covariances and cross-covariances of , and .

<p>Covariances and cross-covariances of , and .</p

Spatial distribution of SIR population fractions at different times: (a) <i>t</i> = 5, (b) <i>t</i> = 10, (c) <i>t</i> = 20, and (d) <i>t</i> = 30.

<p>Spatial distribution of SIR population fractions at different times: (a) <i>t</i> = 5, (b) <i>t</i> = 10, (c) <i>t</i> = 20, and (d) <i>t</i> = 30.</p

BME-SIR standard error for the predicted HFMD rates shown in <b>Fig. 11</b>.

<p>BME-SIR standard error for the predicted HFMD rates shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072168#pone-0072168-g011" target="_blank"><b>Fig. 11</b></a>.</p

BME-SIR predicted population HFMD rates (cases per 10,000 people) in the study region for 4 selected week instances: (a) <i>t</i> = 5, (b) <i>t</i> = 10, (c) <i>t</i> = 15, and (d) <i>t</i> = 20.

<p>BME-SIR predicted population HFMD rates (cases per 10,000 people) in the study region for 4 selected week instances: (a) <i>t</i> = 5, (b) <i>t</i> = 10, (c) <i>t</i> = 15, and (d) <i>t</i> = 20.</p