A stochastic graph process for epidemic modelling

Abstract

A stochastic graph process with a Markov property is introduced to model the flow of an infectious disease over a known contact network. The model provides a probability distribution over unobserved infectious pathways. The basic reproductive number in compartmental models is generalized to a dynamic reproductive number based on the sequence of outdegrees in the graph process. The cumulative resistance and threat associated with each individual is also measured based on the cumulative indegree and outdegree of the graph process. The model is applied to the outbreak data from the 2001 foot‐and‐mouth (FMD) outbreak in the United Kingdom. The Canadian Journal of Statistics 40: 55–67; 2012 © 2012 Statistical Society of Canada

Data‐Driven Models of Foot‐and‐Mouth Disease Dynamics: A Review

“…Some models are quantified with host data at a resolution appropriate for modelling targeted control; however, locations using host data are largely limited to Australia (Pech and Hone, ; Garner and Lack, ,b; Dexter, ; Doran and Laffan, ), Europe (Haydon et al., ; Ferguson et al., ,b; Keeling et al., ; Kao, ; Ap Dewi et al., ; Tildesley et al., ; Kao et al., ) and the United States (Bates et al., ,b; Carpenter et al., , ; Ward et al., , ; Highfield et al., ; Tildesley et al., ). Only a subset of models directly incorporates disease data (Klaring and Timischl, ; Woolhouse et al., , ; Haydon et al., ; Howard and Donnelly, ; Ferguson et al., ,b; Keeling et al., ; Gerbier et al., ; Bouma et al., ; Rivas et al., ; Tsutsui et al., ; Gilbert et al., ; Chowell et al., ; Diggle, ; van den Broek and Heesterbeek, ; Chis Ster and Ferguson, ; Savill et al., ; Estrada et al., ; Tildesley et al., ; Chis Ster et al., , ; Jewell et al., ; Boender et al., ; Deardon et al., , ; Lawson et al., ; Hosseinkashi et al., ; Vergne et al., ); of this subset, the UK 2001 outbreak is overrepresented. Overall, models appropriate for targeted control represent areas where current infections with FMDV are not observed and locations with high FMD incidence are not represented in the modelling literature.…”