Discovery of a missing disease spreader

Abstract This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.

[1]  V. Isham,et al.  Stochastic epidemics and rumours on finite random networks , 2010 .

[2]  Kenji Yamanishi,et al.  A unifying framework for detecting outliers and change points from time series , 2006, IEEE Transactions on Knowledge and Data Engineering.

[3]  M. Safan,et al.  Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan. , 2009, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[4]  M. Keeling,et al.  Integrating stochasticity and network structure into an epidemic model , 2008, Journal of The Royal Society Interface.

[5]  R. Pastor-Satorras,et al.  Bosonic reaction-diffusion processes on scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Yukio Ohsawa,et al.  Node discovery problem for a social network , 2007, ArXiv.

[7]  Hsinchun Chen,et al.  Prospective Infectious Disease Outbreak Detection Using Markov Switching Models , 2010, IEEE Transactions on Knowledge and Data Engineering.

[8]  J. Robins,et al.  Transmission Dynamics and Control of Severe Acute Respiratory Syndrome , 2003, Science.

[9]  S. Riley.  Large-Scale Spatial-Transmission Models of Infectious Disease , 2007, Science.

[10]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[11]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[12]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[13]  Robert D. Nowak,et al.  Network Inference From Co-Occurrences , 2006, IEEE Transactions on Information Theory.

[14]  Ashutosh Kumar Singh,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2010 .

[15]  Matt J Keeling,et al.  Using conservation of pattern to estimate spatial parameters from a single snapshot , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Yoshiharu Maeno,et al.  Profiling of a network behind an infectious disease outbreak , 2009, ArXiv.

[17]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[18]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[19]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Marcello Pagano,et al.  Using temporal context to improve biosurveillance , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Takashi Odagaki,et al.  Effects of superspreaders in spread of epidemic , 2006, Physica A: Statistical Mechanics and its Applications.

[22]  S. Havlin,et al.  Epidemic threshold for the susceptible-infectious-susceptible model on random networks. , 2010, Physical review letters.

[23]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Alessandro Vespignani,et al.  influenza A(H1N1): a Monte Carlo likelihood analysis based on , 2009 .

[25]  E. Lyons,et al.  Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings , 2009, Science.

[26]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[27]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[28]  E. R. Cohen.  An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements , 1998 .

[29]  David M. Walker,et al.  Parameter inference in small world network disease models with approximate Bayesian Computational methods , 2009, Physica A: Statistical Mechanics and its Applications.

[30]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[31]  Réka Albert,et al.  Disease Dynamics in a Dynamic Social Network. , 2010, Physica A.

[32]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[33]  M. Keeling,et al.  On methods for studying stochastic disease dynamics , 2008, Journal of The Royal Society Interface.

[34]  R. Rothenberg,et al.  Network structural dynamics and infectious disease propagation , 1999, International journal of STD & AIDS.

[35]  M. M. Telo da Gama,et al.  Stochastic fluctuations in epidemics on networks , 2007, Journal of The Royal Society Interface.

[36]  C. Fraser,et al.  Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions , 2003, Science.

[37]  M. Small,et al.  Super-spreaders and the rate of transmission of the SARS virus , 2006, Physica D: Nonlinear Phenomena.

[38]  Alessandro Vespignani,et al.  Invasion threshold in heterogeneous metapopulation networks. , 2007, Physical review letters.