Dynamic Random Graph modeling and applications in 动态随机图模型及其应用.pptVIP

Dynamic Random Graph Modelling and Applications in the UK 2001 Foot-and-Mouth Epidemic Outline Foot-and-mouth disease outbreak in the UK, 2001 and dynamic random graphs (DRG) Introducing a Markov model for DRGs Inferring the missing edges and some epidemiological factors Application to the UK 2001 foot-and-mouth (FMD) epidemic Simulation results and detecting the high risk farms Thanks… * Christopher G. Small Joint work with Yasaman Hosseinkashi, Shoja Chenouri (Thanks to Rob Deardon for supplying the data.) At day 4 At day 5 Foot-and-mouth outbreak, UK 2001 All farms involved in the epidemic Farm known to be infectious at the current day New infection discovered Edges show possible disease pathways At day 44 At day 184 Foot-and-mouth outbreak, UK 2001 Date (day) Cumulative number of infectious farms over time Changes in the diameter of the infectious network over time Date (day) Foot-and-mouth outbreak, UK 2001 Infectious disease outbreak as a dynamic random graph The development of an infectious disease outbreak can be modeled as a sequence of graphs with the following vertex and edge sets: Vertices: individuals (patients, susceptible). Edges: disease pathways (directed). Individuals Connecting two individuals if one has infected another A Markov model for dynamic random graphs is a sequence of random directed graphs over a continues time domain T where Model assumptions: Every infectious farm i may infect a susceptible farm j with exponential waiting time . Simultaneous transmissions occur with very small probability. Transmission hazard can be parameterized as a function of local characteristics of both farms and their Euclidean distance. Embedded in discrete time domain: Waiting time to get into k’th state All farms with their active transmission pathways The composition of infectious/susceptible/removed farms changes over time by new infections and culling the previously infected farms. The k’th transition